Not horizontally, anyway.
This is a pretty tricky one to get your head around at first, but once you see it, then it seems like the most obvious thing in the world.
Most people think that a mirror flips your image along the Y axis (i.e from left to right), meaning that your left becomes right, but this is isn't quite true, it's actually you that's doing the flipping, not the mirror.
Imagine you were to write a word on a piece of paper and look at it in a mirror, the word would appear to be flipped backwards, but that's only because you've flipped it around relative to where you're stood.
For example, now imagine that you've written that same word on a clear piece of glass; when you turn it around, the word will appear to be flipped in relation to you in the same way that it is in the mirror.
Our problem comes from the fact we think of mirrors and reflections as two-dimensional, working only on the X and Y axes, when actually, the main culprit of the mirror phenomenon is the three-dimensional Z axis.
Light is travelling between you and the mirror along the Z axis and it is this that is being "reversed", so the mirror isn't actually showing you a flipped version of yourself, so much as an "inside out" one (gruesome).
It's a tricky concept to get across in just words, so if you whip this one out at a party, then a practical demonstration such as in the video above is highly recommended (not to mention a good party trick).