The three major stove types used for lightweight camping are pressurised liquid fuel stoves, gas stoves and unpressurised liquid fuel stoves (ie Trangia). Broadly, pressurised liquid fuel stoves perform the best in cold conditions and at altitude and are much used on expeditions, gas stoves are simple, clean and ideal for summer use, and Trangia fill the same niche as gas stoves but are cheaper to run. However, each category has its pros and cons and new models that extend the boundaries of what each type can achieve are appearing all the time.
If you are confused by the vast array of stoves available, or want information about a stove you have, a good place to start your search is Hikin' Jim's Adventures in Stoving - the blog of a real camping stove enthusiast! Follow that up with a look at larsonweb.com and you will have more information about stoves than your brain can cope with!