Dreams can be fun or scary. Or, in a George R.R. Martin story, they can be totally prophetic or transformative.
Dany and Bran first come to mind when we think about dreams, but everyone else participates, in the fun, too. When Eddard is feverish from his wounds, he tends to dream about the past. (Which is a great way for Martin to slip in these little history lessons for us; see "Setting" for other ways Martin slips them in.) Even Sansa dreams, although her dreams don't always come true; for instance, she dreams that Joffrey will be king (true) and that she'll be queen (not so much) (52 Sansa 4.13).
Sansa also knows that dreams are supposed to be prophetic, so she might be guilty of expressing a wish in the form of a dream:
"I had a dream that Joffrey would be the one to take the white hart," she said. It had been more of a wish, actually, but it sounded better to call it a dream. Everyone knew that dreams were prophetic." (45 Sansa 3.15)
So there's a definite tension about dreams: are they true or not? This tension is characterized by Maester Luwin and Osha, the wildling: Maester Luwin tells Bran that dreams are only dreams, but Osha notes that some dreams aren't just dreams (67 Bran 7.39, 67 Bran 7.65). So who's right? The learned maester or the wildling from beyond the wall?
Shmoop tends to think that Osha is right here and that dreams may be prophetic. And hey, since dragons have returned and a three-eyed crow talks to Bran, maybe this is a fine time for some supernatural dreams.