Firstly, take a classic small iso-butane gas burner. This is a very simple cooker that burns butane/propane gas. There are endless models of these out there, probably the best example I've come across is an MSR Micro Rocket. The basic reason you would use one of these is that they are very simple to use. Screw it onto the canister, light it up, and away you go. This simplicity is why they are easily the most popular style of cooker by sales volume. Butane/propane canisters are available at all outdoor stores, so are fairly easy to get your hands on. However, these canisters are also the main weakness of this stove type. They are relatively expensive ($8-$12 per canister), you can't vary the amount of fuel you take (i.e. you can't only take half a canister), you can't refill them and at the end you are left with a canister that is difficult to recycle. You also can't take the canisters flying.
Pros: user friendly, light, relatively cheap.
Cons: Have to carry a canister with more gas than you may need, the canisters are relatively heavy.