I ran a campaign once where I let my players start out with 12th-level characters, built on 32 points. I specifically warned them to make their characters very two-dimensional and larger-than-life, as I was going for an "ultraheroic", comic-booky feel. Then, halfway through the first session, I collected their characters and quickly statted up 1st-level, NPC-classed, 15-point versions of the same. The paladin became a warrior, the wizard became an adept, the nimble female fighter became an expert (barmaid), and so forth. I then explained to them that these were their "real" characters who had just awakened from a very pleasant (shared) dream, in which they had been running around as idealized versions of the people they secretly wished they could be.
It was a very risky move, and I knew that going in. I was rather scared, actually, but if it hadn't worked, well, we'd only have wasted one session and I could chalk it up as a one-shot experiment. Fortunately, my players absolutely loved it. I split the sessions down the middle, spending half of each session in the dream world and half in the waking world, so they got a chance to play each character. Unfortunately, the campaign petered out when one of my players had a change in his schedule and was unable to make it to the games anymore. Ultimately, I had been planning on dovetailing the two halves together, and having events in the dream world impact events in the waking world, but as it is the characters never progressed nearly that far and in fact never quite realized that they were all having the same dreams. Oh well.
Personally, as far as being a player goes, it really depends on the execution, like most have said. I really enjoy it sometimes, but I've had experiences where the character suddenly wakes up and none of the previous sessions ever happened, or the campaign suddenly switches genres three and four times in rapid successions, and that can really kill the fun.