It's extremely rare for me to remember my dreams. I wish I could remember them more often. I've heard that if you write down your dreams in a dream journal as soon as you wake up you'll become better at remembering your dreams. The problem is, I don't even remember my dreams as soon as I wake up, so I have nothing to even begin writing down. (Plus, most mornings I'm not awake enough to write anything when I first wake up.)
Whenever I am lucky enough to remember my dreams, they're usually quite odd. I think the oddest dream I've ever had was the one where I was abducted by aliens along with the actors from the Harry Potter movies. I also had a pretty weird one that involved our lockers in high school becoming really weird shapes. They were basically jungle gyms that you had to climb on to open and the were all different sizes and stuff. I usually did have a really weird dream related to school the night before I would go back. That didn't happen starting college this year though.
I also wish I had lucid dreams. It's such a cool concept, but the closest I've ever got to that is when I'm half-awake in the mornings, which I don't think counts.