the first computer game i ever really played was fallout 2. so i might be a little biased in this decision... but it's definitely my favorite. it seems like it just has a lot more possibilities than fallout 1...there are a ton of endings you can achieve. you can get extremely involved in the workings of each city. i got lost in it so easily.
fallout 3 was brilliantly designed, but just doesn't have enough quests IMO. after the initial few hours, everything started to look the same. there are only so many times i'll actually open metal boxes/footlockers/lockers and be excited about the possible contents. fallout 2 seemed more limitless.