Discount airlines are also known as no-frills carriers or low cost carriers (LCC) in contrast to Full service or legacy carriers.
Probably the first such airline was Sir Freddy Laker's "Skytrain" of the 70s. In the US, Southwest Airlines  revolutionized American air transport by running fleets with one type of aircraft, the Boeing 737, to save on maintenance costs, and eliminating the 'frills' of air travel. In Europe, Ryanair pioneered the concept  and is now famous for treating its passengers like cattle, having more complaints filed against it than any other.
No airline based and inspected in an OECD country is able to cut corners on safety and most LCC's have very young aircraft fleets.
Discount airlines around the world
See the article on Australia for information on discount airlines flying long haul to Australia.
Some airlines offer budget flights from one continent to another.
Round the world
It used to be possible to travel around the world entirely on low-cost carriers, although true long-distance LCCs are few and far between. A sample itinerary:
A longer route from London to Singapore:
The main danger with booking an LCC RTW is that low-cost carriers change routes very rapidly and, if a ticket along your route is cancelled, or the airline goes bust, the airline may not be responsible for anything more than refunding your money (and most debit cards don't cover airlines going bust and some credit cards only cover amounts lost to over £100) and even that isn't always guaranteed — even if there are no other cheap options for getting from point A to point B any more. Even changing dates is usually expensive or impossible. That's fine if you're going to set points for a short period on an RTW eg 3 weeks - but most travellers go for 2 to 12 months on a round the world flight and change their tickets often - you will need that flexibility. You can try to work around this by booking only segment or two at a time, but many countries require showing a departing ticket on arrival. Other example itineraries: LON>KUL>SYD>HNL>YVR>LON (Using: Pegasus,Air Asia,Jetstar,Westjet and Canadian Affair) LON>FRA>GOI//CCU>KUL>PER//SYD>HNL>NYC//YYZ>LON (Using: Ryanair or Easyjet,Condor,Air Asia,Jetstar,Hawaiin Airlines,Canadian Affair) LON>IST>MAA>KUL>SYD>HNL>YYC>LON (Using: Easyjet,Air Arabia,Air Asia,Jetstar,Westjet,Canadian Affair)
You can access a Low Cost Airline RTW route map here: Round the World with Low Cost Airlines
How to get low fares
Almost all low cost carriers sell their lowest cost fares exclusively through their own website. Phoning them will result in a surcharge or higher fare or they may only offer web sales. However, most discount carriers lack "search engine presence" and home-pages won't appear first in search engines. Avoid consolidation travel sites which appear to offer true discount fares which appear first. These generally don't quote surcharges, taxes and other costs and often cannot sell you the true lowest price as they often earn commissions from airlines. Search for carrier name + "home" to find websites (that is, Google "Viva Macau +homepage")
Don't assume major carriers will not discount. Check the major carriers websites also. Major carriers often have more frequent flights and a higher capacity to fill.
Low Cost Carriers & on-line services
Low cost carriers often impose (very) low baggage allowances. These can be as low as 10-15kg for one item only but some carriers offer generous allowances. Dont assume & check the carriers rules before booking. They generally rigidly enforce excess allowances at check -in and require cash or credit card payment or they will refuse boarding. Don't expect in-flight power sockets, music, video or magazines. Their website may have "on board" information that explains services available.
Parents with small children should call the airline and ensure any special requirements are available prior to booking. Change facilities may be simple or non-existent. Seating options may not be available or be very restrictive (ie bulkhead seats which offer no legroom).
Many low cost carriers do not provide meals, water or in flight entertainment. Some sell these on-board, but not all. With security arrangements changing around the world do not assume you can bring food or water on board. Check their website carefully prior to booking. Some airlines permit pre-booking of upgrades for meals, baggage and other services at a discount at booking. Walk-up payment is often over-priced or the quantity not available to meet demand. Be flexible and prepared prior to your flight. (Tip - Take tissues in case of low toilet paper supply)
Seat allocation for low cost carriers is generally either pre-booked as a preference at the time of booking or is not available until check-in. Once again, check the airline website carefully and read the terms and conditions prior to providing credit card details. To obtain best seats it is essential that you arrive as early as possible to the airport for check-in and seat allocation.
ALWAYS buy reputable travel insurance but not from the carrier. Discount carriers don't always offer credit for missed flights and may also then not offer a discount for travel at short notice. The US$50 fare you pre-paid may be lost and a new fare of $450USD be your only option. Always ensure you know what the airline policy is if you arrive late to check-in as well as sicknesses, illness etc.
Book during sales
Most low cost airlines offer seat sales at regular intervals. This happens particularly during off-peak times of year, such as winter. There can be incredibly good deals on offer during such sales. Ryanair tends to have both the widest choice of seats, most frequent sales, and cheapest fares during such sales. They sell 'free' flights, where you just pay the taxes and charges. The total cost of the flight will depend on what airports you use. The total cost of a one-way flight from London (Stansted) to Milan during a seat sale is €20 (£14, US$25). Flying from less busy airports during a seat sale will provide even cheaper seats, as fees at London Stansted airport are (comparatively) high. A flight from Glasgow (Prestwick) to Rome during a seat sale costs €16.50 (£11, US$20). Fly between even less busy airports (Stockholm (Skavsta) and Hamburg (Lübeck), for example) during a free fare sale and you will pay around €10 (£7, US$12.50).
Other airlines can have reduced prices during sales as well. Find out who flies there and make regular visits to their websites, and register for their newsletter.
Book well in advance
Although it is a good choice to book your flights well ahead, it does not always guarantee you the cheapest fares as it is a myth that the cheapest fares are the first few seats on an aircraft. If there is nothing particularly cheap when you first look, and there is a long time before your trip, you might be better off waiting for a seat sale.
If you are not into making early preparations, sometimes the airlines tend to radically reduce the prices of the very last seats if they haven't been successful in selling those, so you may be able to find a great last-second deal if you're prepared to leave soon.
Fly off-peak if possible
Airlines take advantage of increased demand on tickets during school holidays to increase ticket prices. Flights to Salzburg Airport from London Stansted with Ryanair go up two - three fold during the February school holidays, whereas BA flights from London Heathrow to Munich are half of what Ryanair demands.
Friday and Sunday evening flights tend to be more expensive. Early Sunday morning and and late night flights can be cheaper.
Price wars are your friend
If two airlines are having a price war, then this will work to your advantage. This typically happens when two airlines announce a new route at the same time, and attempt to price each other out of the market. Use a good news source to look for news articles about this or a price comparison tool to find the latest ones. Search for both the airlines and the destination you are hoping to go to. For example, easyJet and Ryanair have a price war on the London Gatwick and London Stansted to Alicante sectors.
Be creative with your routes
The cheapest route is not necessarily the most direct. jet2  flies between Belfast and Prague direct, but you will often be better off flying from Belfast to Gatwick, and then on to Prague from there. It will take longer, but you could save substantial amounts of money. This is just one example, there are many others. Bear in mind, however, that each additional leg does mean paying all the airport fees and charges, plus any credit card booking fee again. Thus two €25 legs could together cost more than a €60 leg once you factor in the extra €20 or so of charges. On the other hand, some airports are particularly cheap - in Ireland the fees are under €15. If you miss a connection travelling this way the airlines won't help you out so could end up paying top whack for a new ticket so make sure you allow plenty of time between connections and also be aware you will have the hassle of going through check-in and security for each flight segment.
If you are flying return trip with a long route — say London to Sydney or Toronto to Singapore — it can still be possible to fly discount carriers. If you were considering a stopover anyway, the connection between carriers may not pose an additional inconvenience or risk.
Tip : Discount carriers generally don't operate between two major airports. For example Sydney - Hong Kong. However Sydney to Macau is serviced by Viva Macau. Transit between Macau and Hong Kong is cheap and fast. Find routes that take you close to major centres using discount carriers and compare transit costs and times. Using the Macau example several high speed jet boats service the route (1hr). Fares are cheap and services are continual day and night. Macau is also well serviced by low cost carriers to Mainland China and other Asian destinations (Japan, Thailand, Singapore, Malaysia) who don't operate out of Hong Kong. Finding those low-cost hubs can be hard but very rewarding. Growing "hubs" that support low cost carriers are emerging in Emirates / Dubai / India and Asia.
Know the airlines
Make sure that you know all the airlines that serve the destination to which you want to travel. As competition expands, it can be hard to know what airline flies where. Keep yourself informed by using the resources below to keep tabs on the situation. Typically, travel agents and web search engines will not search these airlines, as they are not connected to the global booking systems, and do not pay the standard agent commissions.
There are now some very sophisticated websites that offer end-to-end routes (including bus and train services) between any two addresses on planet earth; Rome2Rio is one example.
Go for it
If you see a brilliant deal, just go ahead and book it, even if you're not sure if you will be able to use the flight. Go places you've never heard of, just because you can. Enjoy the low-cost airline boom while it lasts, and have fun.
Use the exchange rate to your advantage
Most flights booked from the airlines website are sold in the currency of the departure port. Booking two one way flights will usually be sold in two currencies, whereas booking a return flight will be sold only in the currency of the origin. The airlines price into a market, and the airfare will rarely be the same after taking currency conversion into account. The saving (or premium charged) can often be as much as 20%. Book whichever way is cheaper. Similarly if you have a stopover, check the fare if you book the same flight originating from your stopover point to the fare if you book all the way through, especially if there have been significant movements in the exchange rate in your home currency's favor.
Hidden Costs and Complications
Discount airlines also try to save money on the services they deliver. You need to factor in these costs and complications to do a comparison between the discount airlines and the full-service ones.
Some carriers such as Ryanair fly to airports that are sometimes well away from the advertised destination. Hahn Airport, risibly called the airport for Frankfurt, is 100km away from the city and so is the Paris Beauvais Airport!
Make sure you factor the cost of transportation to your actual destination, and the additional time it may take. The trip from Frankfurt Hahn to Frankfurt Airport/City is 1.5 hours extra on your journey and the savings compared to BA or Lufthansa are not very high. In some cases the obscure airport might even be closer to where you want to get to.
In-flight food and drink
You will almost always have to pay extra for food and drink on a discount airline. However, free refreshments are provided by Air Berlin and BMI (British Midland). The best idea is of course to bring your own food and drink but some airlines make an announcement pre take off to say that you are not permitted to consume your own food and drink. Whether this is enforced or not just depends on the cabin crew on the day but be aware that the crew earn commission on in-flight sales so may ask you not to eat your own food.
Most fluids are banned from passing through security in airports, so you will have to buy any drinks to take on flights after the x-ray machines. An alternative is to take an empty water bottle on the plane and fill it with tap water.
Outside North America, most low cost airlines operate a "point to point" service. (Notable exceptions include Air Berlin and Wizz) If you are making a journey that involves a change of plane, even on the same carrier, you will have to check your luggage in for each leg of the journey. This also means clearing passport control for international-to-international connections thus adhering to the usual visa requirements of a visitor (as opposed to a transit visa holder) in the country of transit (yes, this means lining-up at that country's embassy in your home country and filing the relevant application fee even if your visa is denied - see the article Visa for more information). In addition, with some airlines (including Ryanair), if your first leg is late you will not be transferred onto another plane if you miss the second. easyJet will sometimes transfer you free onto another flight when the first one is late if you have left a gap of two hours between flights and they are both easyJet flights. However, their carrier regulations  do not guarantee this. It is wise to check with each airline their policy on missed connections. You can insure against missing low cost connections with travel insurance.
Making low cost connections can often work out significantly cheaper and in many cases is the only way of getting between two European cities. For example, there are relatively few direct low cost flights between Northern Africa and Eastern Europe. You will most likely need to fly with Ryanair to an airport like Marseille or Frankfurt (Hahn) or with AirBerlin to Germany, and then another flight on from there. Flying indirectly between two cities can often work out cheaper even if there are direct routes.
Factors such as the distance between terminals, the reliability of the airline into the airport, the length of time needed to clear security and customs, and the required advance check-in time should be considered when calculating how much connection time you need. Being risk averse may mean allowing up to 3 hours for a connection.
There will usually be restrictions or costs on making changes to your booking. A fee is usually charged in addition to any fare difference between the flight you have chosen and sometimes the total cost you spent on amending the trip and purchasing the lower-cost ticket can well exceed the cost of the full fare. For low cost airlines in particular, they often allow no changes which means that you will have to forfeit your ticket for the original flight and buy another one for the new date or time. There are often restrictions on how close to the departure date and time you can make changes. Hence if you are availing of promo and/or restricted fares, it is extremely important that you are absolutely certain that you will travel on the date you originally chose. See the airline websites for information.
Check in baggage
Many discount airlines charge additional fees for any check-in baggage at all. Others have lower size and weight limits, after which high fees are charged to excess baggage.
As a side-effect of charging for check-in baggage, they can also be more strict on the weight and size of carry-on baggage.
If you intend to use a budget airline as just one of your flights for the day, they may not offer check-through to your final destination. This means claiming your luggage at your transit point, clearing formalities (and if necessary, obtaining visas in advances), and lining-up at the regular check-in counter of your next flight.
Frequent Traveller Programs
Many discount airlines have loyalty programs which reward their frequent travellers. Southwest Airlines has a "Rapid Rewards" program where each flight is a credit. 8 credits will earn you a free flight. Credits may also be earned through an affinity credit card. Credits expire after a certain period of time. Credits may be redeemed for free flights with comparatively few blackout dates (16 total blackout dates in 2005) and with no capacity controls (unique in the industry--in other words, any open seat may be ticketed with award credits), or for a companion pass. AirTran, JetBlue, Frontier, Air Berlin and Germanwings are other airlines offering a loyalty scheme.
Airlines often tie up with local transport and hotel groups who offer discounts if you book having been referred by the airline. As always it pays to use the Internet to do some comparison shopping, but frequently you will be able to get a discounted car-rental, train ticket or hotel room by clicking on the links after you have purchased your flight. The catch is that many of these discounted prices are extremely inflexible, non-refundable and require payment in advance so try not to change your mind after you have made the booking.