In the 1945 Professional football championship game(Washington Redskins and The Cleveland Rams), Steve Bagarus(DB-HB) wore “00” for the Champion 'skins.
OK – here’s what I found.
The Official FIBA rules (PDF!!) say:
(Bolding mine)
While the ULEB regulations (Also PDF!! :() (which can be construed as a “National Federation” for the purpose of EuroLeague play) say:
So 20 and 40 (which I’ve seen) are OK. Supposedly the choice of numbers allows unambiguous signalling by the referees, although I’m not clear on why it helps… 
I can’t find the Israel Basketball Association regulations right now, but I’m pretty sure they follow ULEB.
The upshot of all this is that European Basketball now allows the use of “00” (but not just “0”!) as a Jersey Number.
Dani
My dad had told me 30 years ago double zero meant double trouble, so I went with it on the field. I have no clue if its true but I sure tried to live up to it.
I can’t remember who, but in baseball, I recall a catcher wearing 00. I also recall something about him being asked why that number and he said something about balance behind the plate.
I’ve heard that story, specifically attributed to Benito Santiago, who originally wore 9, and then switched to 09 for several years, ostensibly to “balance” the sides of his jersey, or (another explanation I’ve read) because he didn’t like how the vertical strap on the back of his chest protector bisected the “9” on the back of his jersey.
Baseball has had twenty players wear 00, including some pretty well known players, like Jeffrey Leonard, Jose Canseco, Jack Clark, Bobo Newsom, and Don Baylor.
The 1985 Toronto Blue Jays had both a 0 (Al Oliver) and a 00 (Cliff Johnson). Rather unsurprisingly, that is a unique situation in baseball history.
Recognizing that this thread is a 17-year-old zombie…
As was originally noted upthread in 2005, the NFL made significant changes to their rules on uniform numbers in 1973, with certain ranges of numbers reserved for certain positions (e.g., 1-19 was only for quarterbacks and kickers, 80-89 was only for wide receivers and tight ends, etc.). As part of that standardization of uniform numbers, the numbers 0 and 00 were no longer allowed, though Jim Otto and Ken Burrough were both grandfathered in.
Over the past decade or so, the NFL has loosened up the rules on jersey numbers, including now allowing players such as wide receivers, running backs, and defensive backs to wear numbers 1-19. However, 0 and 00 are still not allowed.
If I recall correctly, they platooned as DHs. At least in the playoffs against the Royals.
Robert Parish was Double Zero for the Celtics.
Now the thread’s basically dead, the topic reminded me of the great, yet extremely obscure song Zero Zero by Witness.