My dreams generally switch between first person and a more omniscient point of view. They're usually really realistic; meaning I can feel, smell, etc. It's really interesting actually and sometimes I wish I could record them. I get the story-line sometime too, like Anaxilea said. Where the story breaks up between several different dream sequences. Sometimes the stories get broken up and I won't dream about them again for years at a time.
A lot of times though my dreams are connected to memories that I've blocked out for whatever reason. They always seem kind of encrypted though... For example, only one or two parts will be connected to a memory and the rest will basically be nonsense or gibberish from present events or something I've been exposed to recently. I always wake up knowing which part was the memory though. It's kind of a surreal experience.