A few weeks ago, my SF-writing class critiqued a story that began with the protagonist's dream. The question rose: Do editors dislike -- or even "automatically reject," as one student had heard -- stories that start this way? Since I didn't know the answer, I emailed three editors, of which two responded.
Stan Schmidt at Analog said that he does not automatically dislike stories that begin with a dream sequence, although "it's a technique that beginners seem relatively likely to use poorly." He went on to say that "sometimes it can work very well indeed," at the beginning or anywhere else in the story. Stan once ended a story with a dream (he did not, alas, name the story in his email.)
Gordon Van Gelder at Fantasy & Science Fiction was more vehement ("Why oh why do writers keep coming up with stuff like this?") His stance was basically "it depends" -- how well is the dream is done, is it related importantly to the rest of the story, is it happening to a character he can care about. Gordon also included the interesting sentence "It's been so long since I read a story that starts with a dream sequence that I really don't know how I feel about them in general." That suggests that the slush pile is not overflowing with this technique.
I have started stories with dreams. My own take is that it can work if (1) the dream is kept short, (2) the description of it contains arresting images, and (3) it's completely clear when the dream is over. Usually I set off a dream sequence in italics so there is no confusion.
So -- dream on.