I find it irritating when the ending you get is influenced solely by one dialog option at the end, and nothing else. E.G. Fable, Mass Effect, Deus Ex 2. If you're going to, as Zhoomout says, artificially lengthen your game, you should at least make it so that the player actually has to play the game again, and not just load the savestate you made before the final battle and click on something different. Bioshock was also terrible for this, but on the other end of the scale. You harvest one little sister to see what happens, and bam. You're a psychotic megalomaniac who wishes for nothing more than death, destruction, and six different types of rape for all humanity. It just doesn't make sense when you've been a paragon of virtue for the majority of the game.
I can't remember how it went in the Kotors. I think it drew from your affinity? Either way, there was enough difference in how you got there to make it worth replaying - there were several different roles Bastila alone could play - so it did manage pretty well.
I miss the endings from the old REs. They depended on the actions you made throughout the game. I hear Dead Rising didn't do it too badly, either.
Edit: Oh, I was beaten to the punch a little. Ah, well~