I've used old fashioned liquid fuel stoves, a Gigapower gas canister stove, and one attempt at an alcohol stove. You can refill liquid stoves by buying more fuel, but these stoves are not light; I'd say their best use is for car camping. You can't refill hiking gas stoves, but you can pick up more cans just about anywhere that sells hiking equipment. Coleman stove fuel is easier to find, but those stoves and fuel are not really light enough for hiking IMHO. They're also ideal for car camping.

Most lighweight hikers end up using alcohol stoves. I think they're okay if you use a good windscreen, and if all you intend to use them for is for heating up water. I prefer gas canister stoves for real cooking, and for the convenience factor. Denatured alcohol is easier to find, though.

I'm not convinced alcohol stoves offer any weight savings over many gas canister stoves... I did a calculation of weight for a Giga stove with a full canister vs. a few of the popular alcohol stoves with an aluminum windscreen, pop bottle to hold fuel, and enough alcohol to match the canister (about 12 meals). They were about the same! Has anyone tried weighing both types of setups to see how they compare in real life?