As the other answers pointed out, there are a lot of urban legends related to mirrors and reflections. And also, whenever we look in a mirror, we see ourselves, but everything is inverted (Horizontally). So horror movies may employ this observation to show that we (or someone) is seeing a laterally inverted personality or character (for example, it may symbolize the good person looking at the mirror and seeing the "bad" version of himself).
And I think also that there's a common [superstitious?] saying that many ghosts are seen only through mirrors and camera lenses. That may explain why [in movies], some persons look in the mirror and instead of seeing themselves, they see a ghost of themselves (or a ghost standing besides them)- a previous life of themselves or an exactly similar situation that happened before, but which ended in tragic circumstances (the mirrors have "trapped" the situation).
Also on a more logical note, from ancient times, mirrors have played a popular role of "demon doors". The reason for that may be that in ancient times, reflections are so supernatural-looking to ancient people and what they may have seen would be an alternate reality. Hence treating mirrors as gateways to demons and gods.
Anyway, that's what I think.