The Standard: For the vast majority of three-season backpacking trips, a canister stove is the best choice. These small, lightweight burners–usually weighing only 3 to 6 ounces–are easy to light and operate, and require little or no maintenance. They also offer the best flame control, which lets gourmet cooks simmer, sauté, and otherwise fine-tune delicate dishes. These stoves run on pressurized canisters of gas (usually a propane/butane mix) that are easily recycled.
Variables: Most canister stoves perform poorly in temperatures below 40°F, and their small size and configuration (burner on top of canister) generally makes them tipsy under large pots of water. If you're cooking in winter or for groups, consider a liquid-fuel stove; white gas performs reliably in bitter cold, and white-gas stoves are much more stable due to their separate-burner-and-fuel bottle configuration.
Going ultralight? Some hardcore ounce-counters swear by tiny alcohol stoves.
Advantages: widely available and inexpensive fuel; superlight stove construction (one popular version is made from a Pepsi can); and minimal bulk.
Disadvantages: reduced cooking power (alcohol doesn't burn as hot); invisible flame; and minimalist cooking surface.
Key Accessories: Most liquid-fuel stoves come with windscreens and heat reflectors. Use them: They improve fuel efficiency and boil times significantly. Windscreens can also be used effectively with canister stoves, but do so cautiously: Overheated canisters can explode. Other essentials: A spare lighter tucked in your first-aid kit; a pot gripper; and (for canister stoves) a folding stove tripod.