Small details, usually, but if something happens in my dream about a specific person that makes me have a certain feeling I almost always remember it. For example, I was talking to this girl at the time, and it was this strange dream of homeless people living in my backyard, and they threw a party, and the girl I was talking to was suddenly hooking up with tons of other guys. I don't remember much else, but I remembered that feeling of that girl hooking up with other people, which allowed me to remember that.
I also remember this one dream about a vacation resort. I went there with my family, and I tied myself up to this giant glass... thing? And suddenly, the biggest tsunami wave I've ever seen washed over me (and everybody else), and it was the most fun i've had in a dream. It kept happening, over and over, and when it was over I was quite sad. I guess the fun feeling make me remember that one.
So, I guess feelings make me remember.