The four characters with whom you can have a relationship are: Alistair, Zevran, Leliana and Morrigan. It also comes in a bit handy since forming a relationship is an easy way to get a lot of approval quickly.
You’ll just get some new dialogue for your ending and you’ll get to see one of the character’s in their underwear.
Note that this does not serve a noticeable material difference for the game. There are four Dragon Age Origins romances that you can pursue.
