People dream in colour, but they remember their dreams in black and white. Apparently, it's because the brain forgets the colours. For those of you who remember their dreams in colour, it's probably because you guys remember the dreams themselves and put colour in them.
Another strange thing about dreams is that you only remember a portion of them. You don't remember the enitre dream, just a few seconds of it; as if the dream itself was only a few seconds long. Not sure why this happens, though.
To answer the question, though, I dream in colour, but I remember my dreams in greyscale. I don't bother to put colour into my memories, since I'm lucky to even remember the dream. Sometimes, I don't remember my dreams, no matter how amazing they are.
I could go on for ages about dreams, since they're so amazing, but I think I'll have to stop here. xD