Fallout 1..... hm.... I like faction fights, so I'm thinking quests like the whole Gizmo vs. Killian Darkwater-story, the Decker vs. Justin Greene-story and Regulators vs. The Blades-story. Those are three good quests (or actually, there are a bunch of quests concerning them) that I remember from Fallout 1. It was so long since I played it, had to look at the wikia to get the names right
Fallout 2... I like the gang war in the Den. I also like (with the Restoration Project) to help Mom set up a home for the homeless children that survive on pickpocketing and handing it over to that very impolite dude.
Fallout 3... A bit harder for me to remember any good quests. Blowing up Megaton shouldn't really have been such an early quest imo. You just get to town, you are very very inexperienced, and you can activate a nuke right away for like the cheapest price ever? Also, it removes the possibility to find out the lore behind the town and finnish a lot of quests. Sure, you can wait with blowing the town up but it kinda urges you to since you can do it so easily right away. Shoulda had a higher skill required, and much more money in it. Oh, and also people getting suspicous about you tampering with the bomb. Anyways, rant over. I like eh... The Replicated Man? I like dealing with that ghouls vs. Tenpenny-quest, I like the slaves vs. slavers-quest. But they aren't really that memorable to me, I am looking over all quests in the Fallout wiki, trying ro remember them and... Well, I do like the quests in The Pitt (if only not so linear) and Point Lookout alot! So I'd say those DLC's are my favorite quests.
Fallout: New Vegas. LOADS of awesome quests. Especially the side quests. Beyond the Beef is really a beautiful quest. Heh heh.