True multiple choice endings which are a consequence of gameplay-I'm ok with. Binary endings I actively despise (Screw Fable, screw Infamous, screw Dishonored). I really don't want to have to play through the thing twice to see the endings. Ending-o-tron things like Mass Effect or Deus Ex earn less of my ire, since while they're binary, they make it relatively simple to view multiple endings. I prefer not to have to go to youtube, to avoid playing half the game again at only a slight variation to gameplay, to find it out.
I prefer if they're going with the multiple endings gimmick that they scrap cohesive coherent cutscenes, and go with copy-paste approaches like the conclusions to Fallout New Vegas (Which I haven't personally finished yet, I'm going by Let's Plays), where it shows the consequences. Or games like Alpha Protocol, where the changes to the story are noticable, and actually seem to have an impact (Too bad it also sucked, wish there was a sequel). Good multiple endings requiring replay actually have actively changing gameplay, and more than one choice. If I'm just straight up paragoning or renegading my way to the appropriate ending, I'm bored as fuck. Rather than making choices about the game, I'm metagaming the heck out of it, and I lose all interest in the story.