Most backpacking stoves don't use propane.

There are 5 primary categories:

1) White gas (Coleman fuel) - still the most reliable in cold weather, but somewhat heavy. High power flame.

2) Cannister - contains a mix of butane and other gases. Simple to operate. Relatively light. High power flame, but drops in intensity in cold weather. You cannot get these refilled that I know of.

3) Alcohol - denatured alcohol burns itself reasonably well. Often the stove is a homemade affair made from a couple of soda cans shaped so as to maximize their heat retention and air flow. Weighs less than an ounce. Lower power flame.

4) Solid fuel - esbit, trioxane, etc. "Heat tabs". Light them and they burn. Stoves range from a 1/4 ounce to 2 or 3 ounces. Simple, very light, stinky. Lower power flame.

5) Wood burning stoves - some with battery powered fan (zipstove); others with special air flow design to maximize oxygen and heat (bushbuddy). can soot up pots very quickly. Only requires natural fuel. Medium to high flame.

There are proponents of all types here.

I probably use the cannister stove most often nowadays. On long-distance summer trips, I still like the light weight and simplicity of my esbit stove. In really cold weather (20 F or lower) I carry the weight of my white gas stove (MSR Whisperlite) because cannister take a good bit of futzing and warming to work well when it gets this cold.

Alky stove users will certainly let you know about the benefits of the alky stove. They're intriguing but not quite right for me.