I really hate these dreams. I always wake up thinking of the dream as memories from the day before. I don't know how many times I've started talking to people about things I did yesterday only to have them tell me nothing I remember actually happened.
As for strange dreams.. I don't really have any but as did a weird recurring dream where, I think, I was in a cave with Zelda from the video game series. We were searching the cave for some treasure. Nothing was ever said, but I could just tell that's what we were looking for. We eventually find a treasure chest and I run over to open it. As soon as the top is lifted I fall to the ground unable to breathe. Then the "camera" of my dream pulls back and I'm lying on my living room floor in front of my SNES gasping for air and calling for help. Used to scare the hell out of me.