If you are claustrophobic or have long legs, specifically ask the travel agent to book you an aisle seat. That way you can only be 'boxed in' on one side and you can get up and stretch your legs during the flight without having to climb over your neighbour.
Don't take more luggage than you can carry by yourself. Airports generally have baggage carts for rent, but you have to have local currency (usually coins) to use them.
Beware of luggage weight limits. Not all airlines have the same weight and size requirements. It is quite possible to get halfway around the world with your two bags and then to discover that they are too heavy/bulky for your next airline to carry them. If you are planning a long trip, make sure that your luggage meets the strictest limit before you start.
Don't overpack. It may be tempting to take as much as you are allowed, but you will want to purchase souveniers enroute and you will inevitably have more baggage on the homeward route than when you left.
Don't lock your bags when you check them in at the airport. In these days of strict airport security, more bags are inspected manually, and if there is a lock on the case they will break it. If you are worried about the security of your baggage enroute to the airport, unlock the case at the counter before you check it in. After inspection and xray, bags are generally 'locked' with a plastic tie so that nobody can tamper with them.
If you are carrying any valuables, put them into your carryon bag rather than your suitcase.
Take a large bottle of water with you. Aeroplane cabins are very dry and you need to drink plenty of water to avoid dehydration.
If you are hypoglycemic, diabetic or have bloodsugar issues that require regular snacks, take your own food with you. Don't count on being able to buy it at the airport either. If you have a tight connection and have to cross an entire airport, there is no way you'll have time to stop at the cafe as well. You will probably be fed on the plane, or offered the chance to buy food, but not necessarily. In these days, more and more airlines are NOT offering meal services.