The one I always hated in Fallout-3 was the one where a poor wastelander would run up and say that the raiders had put a bomb on her.... inevitably I'd fail to disarm it and the wastelander would bravely run away from me to save my life.
What made it even more frustrating was that I had a (modded) piece of gear that would augment my explosives skill (which I normally never bother to raise) but before I could swap into that gear I'd be locked in conversation mode with no chance to put it on. Sorry, lady.
One thing, I don't know if I like it or not... but there were specific places where you would encounter a 'random' event when you approached. Once, while approaching the Super Mart / Greyditch / Wilhelm's Wharf area, I got the random event of the alien spacecraft exploding overhead.... but it hit a building, and rained down the blaster and alien ammo into the area I could not physically reach. So I reloaded and the next time I approached that area, it was just the wounded Deathclaw encounter.... I reloaded the approach to the Anchorage Memorial "island" over and over and over until I finally got the alien crash THERE, where I could collect all the bits properly.
So, as I said, I don't know if I LIKE that the 'random' events happen at ~specific~ places or not. The purist in me says that that sort of doesn't make them really random... I mean, the event itself is random, but if something always at that spot, it's less random-seeming. The min-maxer in me, however, realizes I can just save, approach the trigger point, then reload to get a different, potentially better, 'random' encounter the next time I approach the area.