There are two basic categories of stoves, liquid fuel and gas fuel. First gaseous fuel, things like Gaz
and other brands where the fuel comes in a canister that you attach the stove too. There are two more categories in this one, detachable and not detachable. The detachable ones have a valve on the canister that you screw the stove on and off of. In non-detachable ones, the stove punctures the canister, and you have to keep it attached until the canister is out of fuel. I really, really don't like canister stoves
. The make a lot of waste, you have to haul the canisters around, and I consider them dangerous. Leaving the gas on an unlit stove can be very dangerous, since most fuel gas sinks in normal conditions, it pools and you can accidently ignite it.
Now liquid fuel ones: they run on a variety of fuels, white gas, kerosene, gasoline, alcohol, etc. The fuel is an important consideration if you aren't camping in North America. White gas will be hard to find, kerosene and gasoline pretty easy. In general, however, white gas (essentially just ultra-refined kerosene) burns cleaner and better than kerosene. Gasoline is not fit to burn in anything except an emergency. Alcohol stoves, rare these days, require a lot of fuel, and don't really get that hot. Stoves can either have a base where fuel is poured, or can have a hose that attaches to a bottle. I much prefer the kind that attaches to a fuel bottle, they eliminate the need for pouring, and are easer and safer to store. Liquid gas stoves mostly work by heating the input pipe with liquid fuel, until it becomes gaseous, at which point it sustains itself. Main disadvantages of liquid fuel stoves are the risk of spill (which is why fuel bottles are mainly carried outside the pack) and the fact that they're a tad complex to use.
There are also solid fuel stoves, for example Sterno. They burn what is essentially napalm. I don't like them either, they generate lots of trash. They are, however cheap. The fuel can get expensive though. another problem is that once a fuel chunk or can has been lit, you really can't put it out and save the rest for later. all in all. Solid fuel stoves tend to be heavy because of all the fuel and canisters you have to carry, but OK for short trips.
Without a doubt in my mind, the only brand of camping stove I would condone is MSR (www.msrcorp.com/stoves). I like the Whisperlites, they're light (11 oz) and burns white gas (and kerosene, depending on the model) and only cost about US$80. They're a little tricky to use, but once you get the hang of it, you can be cooking in 3 or 4 minutes. For real gourmets, you might try a MSR Dragonfly, which lets you adjust temparture a little better and burns more stuff, and for real hard core types, the MSR XGK can burn everything from white gas to brandy, jet fuel, diesel,paint thinner, whatever you got. It'll set you back about $110 though.
Regardless of what stove you buy, be careful with it, don't spill fuel, and if you do, for god sake, move the stove over.
Thanks to Accipiter
for reminding me about solid fuel, and wertperch
for a few typos.