Whilst travelling with friends or organised groups is fairly common, by choice or by necessity many people travel alone. Travelling alone is a unique experience and can be a very rewarding way of travelling.
Travelling alone is not uncommon and most solo travellers are able to meet other travellers at hostels, bars, organised tours or any place where travellers tend to hang out.
Advantages to travelling alone:
You automatically get points for having balls, especially if you're a girl.
Your time and budget are your own! No staying in budget flophouses with cash-strapped friends when you love five-star hotels. No staying in five-star hotels with rich friends when you want to save all your money for beer!
It's easier to make friends with the locals. A person by herself is often less intimidating to approach. You didn't come all this way just to talk to the same people you see all the time back home, did you? Make new friends!
More space to make your trip entirely your own. Drink it all in. Reflect. Write in your journal. Solo travel can be great opportunity to (theatrical sigh) "find yourself".
Disadvantages to travelling alone:
You'll get lonely. For sure. But if you plan for it, you can deal with it.
There's nobody to watch your back. And there's no one to watch the luggage while you go buy train tickets. You have to carry all your gear yourself.
It's more expensive, as there is no one to share costs with. Rooms are usually about the same price for one than for two. You'll need to budget a little bit more.
Some destinations lend themselves better to solo travel than others. Being the only loner on a romantic tropical beach, watching happy couples frolic and feeding each other BBQ prawns can lead to thoughts of suicide. Cities, with their bustle of activity, are much easier to be alone in.
Try to pack as light as possible. When travelling with friends, it's convenient to have one person sit and watch the gear while another waits in line for train tickets, buy drinks, goes to the bathroom. By yourself, you'll probably have to carry your things with you.
Hotel rooms are typically priced at "double occupancy", and don't expect them to cut the price in half (or even a little) just because there's only one of you. Hostels are much more accommodating of single travellers, but at the cost of your privacy, charging by the bed in shared rooms.
In places where accomodation is expensive, you can often try to team up with other single travellers to share a room. A good place to meet people that might be interested in sharing a room is on the bus/train/plane in to a new place. Take advantage of the ride to chat up the people around you. Be cautious about who you trust, obviously, but it can be a great way to save money.
The more traveller-y the accomodation, the easier it will be to make new friends. If you're feeling lonely, head to a hostel, not a five-star hotel. Hostels are normally filled with solo travelers, many of them looking to make a friend or two to enjoy a beer with.
Tours can be a great way to meet other travelers
Travel forums can also be a good way to meet other travelers who are in the same destination as you.
A good book is almost like a friend. Have a good book on hand to pass the time when waiting for the train, eating alone, or a quiet night in your guesthouse. It's surprising how much a good book can stave off the blues.
Buy someone a beer! Start up a conversation! Even if you're not outgoing at home, now is the time to start. Ask someone that looks like they've been there a while about cool things to see. Politely offer help to someone just arriving, if you know the hotspots (but don't be overbearing. Nobody likes a "been there, done that" travelling know-it-all.) Better yet -- talk to the locals. In some countries, guesthouses are staffed by young people who like making new friends. Ask a local to teach you a few phrases in her language. Ask a local how to make a toast in the local language. Don't be afraid: at worst, you'll never see these people again, at best -- you'll make a new friend.
Appearance matters. Because you meet a lot of people in a short amount of time when travelling, it helps to put your best foot forward. You don't have to look like a supermodel, but being neat, clean, and smelling good always helps. In some parts of the developing world, people are baffled by the slovenly appearance of some travellers. If you had enough money for a plane ticket to another country, costing more than a local will make in a year, surely you have enough money to launder your clothes, or buy a shirt without holes in it! People will judge you by your appearance.
Smoking may be out of fashion in North America, but in a lot of the world, offering up cigarettes is not a bad way to strike up a conversation.
Life is for the living, so don't go crazy with worrying, but a few simple measures can make your solo trip a lot safer:
If at all possible, arrive at a new place in the daytime. This will give you time to scope out accomodations and get your bearings in the relative safety of daylight. Some places are fine in the day, but dangerous at night. Some places are dangerous in the day, but imagine how much worse they are at night!
Keep a spare stash of cash and other important things, in a different place than you normally keep your money, as you have no one to spot you if you lose your wallet or have your things stolen.
Pay attention to your instincts. If your gut tells you not to get into that cab, take another one. If you have a bad feeling about a neighborhood, a hotel, a person, stay away. Your intuition often picks up on tiny signs of danger before you consciously identify them.
Be careful about drugs and alcohol. You don't have anyone to watch your back, or drag you home if you get too drunk to walk. It's a lot harder to make good decisions about who to trust, where to go, what to do, if you don't have your wits about you.
If you're in a semi-dodgy place for more than a short time, try to develop relationships with locals you trust. If you find a good taxi driver (who isn't driving drunk), ask him if he's available to drive you on other days. If you find a good guesthouse/hotel where the staff seems reliable, stick with it. Find a favorite bar, make friends with the barman -- someone who will stick you in a cab when you're too drunk, and who won't set you up to be mugged in a back alley.