Betrayal at the House on the Hill is another game that I think is interesting to look at; it has characters that fit all the horror tropes, but you never really hear people play it and talking about what their character did: it's what they did.
Of course, that happens with true roleplaying games as well. In the case of BatHotH the issue is just exacerbated because it's clear at some point that they were working on the story for people to get into and I've never actually seen it happen: the stories that arise are always due to mechanics (and only when mechanics work in unexpected ways), not character-building.