While looking for the answer to another question, I have stumbled upon a weird curiosity in the Pathfinder (and presumably 3.X as well) RAW.
Unconscious
Unconscious creatures are knocked out and helpless. Unconsciousness can result from having negative hit points (but not more than the creature's Constitution score), or from nonlethal damage in excess of current hit points.
The condition itself does not cause someone to automatically fall prone. Neither do the most common causes of becoming unconscious, such as Dying or Non-lethal damage, nor less common causes, such as the Brawler's Knockout ability.
Now I wonder if I have overlooked something somewhere, since PF rules are known to be all over the place (hello, touch spells).
While any sane GM™ would probably reply to the titular question along the lines of "Yes, of course unconscious creatures fall prone, they're effin' unconcious!", this is not subject of this question. I'm only interested in the rules here, for the sake of interest and for finding the RAW answer to the question linked above.
Best Answer
According to the rules as written and, yes, it's as silly as it seems,
Unconscious creatures don't automatically gain the condition prone.
Proving a negative is all but impossible, and somewhere among the millions of official Dungeons and Dragons, Third Edition and 3.5 words and the subsequent millions of official Pathfinder words, there's probably a rule that assumes, implies, or maybe even states that unconscious creatures gain the condition prone upon gaining the condition unconscious, but I'm unaware of such a rule, and enough has been written about that rules quirk (and even more about the quirks of the condition dead) that I'd think someone would've found it.
Whether this is an oversight or a case of the writers presuming common sense on the part of their readers, we'll likely never know.
Note that the Rules Compendium for Dungeons and Dragons 3.5 does say that
Why the RC doesn't use the actual word prone here when it freely does elsewhere is a mystery.
(As an aside, while one's unconscious (or dead) one doesn't apparently gain the condition blinded either. Make of that what you will.)