Alcohol stoves are cheap or free to make and use an inexpensive and renewable fuel source. They are extermely light and well suited for bicycle touring and hiking. The basic principal is that if you burn a flammable substance within an enclosed area heat is concentrated and can be used to boil water.

Tin Can Stove
Take an 8oz can of tomato sauce (the short and squat type of can), remove the lid and use the sauce to make chilli or something good. Wash it out and dry. Add some alcohol. Light it on fire with a match. This is the simplest and easiest of stoves. When done cooking you can pour the alcohol back into your fuel canister.

Pot Stand
With either stove it helps a great deal to construct a pot stand. Sometimes natural rock outcroppings or wood can come in handy, but don't count on it. The best design I have found is made of hardware cloth. Instructions can be found at: http://www.kruegerservices.com/fritz/osp/pot-stand.html. If following the stove design above, make the stand 3 and one half inches tall. This will leave space of approximately one half inch between the top of the stove and the bottom of your pot. For a one quart pot I have found a circumfrence of 14 inches works well.

Putting the fire out
The flames can be extinguished by covering the top of the stove with the bottom of a pot, thus depriving it of oxygen.

Fuel
The best fuel is denatured alcohol, which is pure alcohol with poisons in it so they can sell it without paying taxes. Denatured alcohol can be found in hardware stores in the paint section. Rubbing alcohol which is 90% works. Grain alcohol works. That's about it.

Storage
The tin stove fits snugly inside of the pot stand which fits inside of a one quart pot. Obviously this makes for efficent and handy storage.

Sources
http://www.kruegerservices.com/fritz/osp/index.html
http://wings.interfree.it/html/main.html