I'm fine with multiple endings, so long as they feel both substantially different to one another, and feel like a conclusion to the choices the player makes to bring them about.
Several people have already mentioned what I consider to be a particularly bad example; Human revolution, which gave 4 endings that all consisted of speculative monologues, that didn't just fail to explain their consequences, much even specify them. For all that has been said of ME3, it's endings were at least significantly different in terms of outcome, its failing wasn't the endings per se, but its failure to expound on them in any way.
I think context matters, and since in theory multiple endings require context based on player choices, multiple endings are fine, so long as they are substantially different.
Having said all that, a game that's not been mentioned here yet is Nier, which with one exception actually lacks any kind of narrative decision making, but instead on replays does little more than make the enemies intelligible. This design choice changes the plot so significantly than despite it's first two endings being essentially identical, the change in tone actually alters its entire meaning, and makes the whole game much more morally ambiguous, not to mention the fourth and final ending gives a meta-spin on the concept of making sacrifices.