The video has been released to certain news agencies, and Fox has put it up, freezing it before the critical moment. The video, with Arabic writing on the screen, shows Saddam in a long black overcoat being walked, handcuffed, to the gallows by about four or five men wearing black balaclavas. The rope is huge and thick - the noose is enormous - and one man holds a black cloth around Saddam's neck before the noose is placed around it. Saddam is not fighting back, and does not seem to be reacting, really, either way, though at one point he does have an exchange with the hangman. Two men put the noose around his neck, and tightened. At this point the videotape freezes; according to Fox it seems that they received the video that way, frozen at that moment. They are replaying continuously; it last for about 45 seconds. It showed at approximately 3:55 a.m.
Fox has been going live to Baghdad to hear updates from correspondents Clarissa Ward and David MacDougal; apparently this video was released to Iraqi TV and has been broadcast repeatedly across the country, stopping before the actual execution is shown.
Update: MSNBC does not appear to be showing the videotape, and is currently running a documentary on Saddam; they just featured Judy Miller. CNN seems to be showing a repeat, since they've got Anderson Cooper talking to an Iraqi official and saying, "So there are no plans yet to release the footage?" (NB: TVNewser says that CNN International was actually first with the video, as does a commenter here; when I clicked over it was already about 15 minutes after the Fox broadcast.) Headline News doesn't appear to have it either; right now they're looking at capital punishment around the world. In the crawl, Fox is reporting that President Bush was asleep when Saddam was executed.
Update: MSNBC.com does not have it but CNN.com has a still image, plus the video online.
Update, Saturday morning: E&P has a thorough round-up of which newspaper sites showed what when; apparently USA Today and the AP showed pictures of Saddam after his death.