Birds fly into windows becauase they can't see the glass. Instead they often see something reflected in the glass, such as trees or grass if your window looks out over a garden, and think they can fly towards that. This is why they so often fly into car mirrors too, as you get a very bright reflection with these.

The RSPB recommend that you fix a poster or other piece of paper over your window if you have a problem with birds flying into it. They should see this more clearly as an obstacle, and will then avoid the area around it.

In fact you can even get a window sticker which is shaped like a bird. The RSPB say that these work even better, though I wonder if a bird would really 'see' a bird picture as another bird! They would probably just see the general shape and avoid it.