Right now, 17,889 people are playing Gears of War 3's campaign on an online-connected Xbox 360, according to the in-game stats we're looking at with our advance copy of the game. The game comes out on September 20. It's the 19th here in America and in Europe, the two biggest markets for the game.
Technically, the game is already out in Australia (as of two hours ago) but as with most big games, the safe bet is that many of these copies are being playing in places where Gears of War 3 hasn't been officially released yet.
The numbers we can see in the game are only for people playing public matches, whether joinable for the campaign or in the games non-story multiplayer modes. Of those latter modes, there are 2,497 people playing Team Deathmatch, 129 playing Warzone, 166 playing Execution, 127 playing Capture the Leader, 474 playing King of the Hill and 85 playing Wingman. There are zero people playing Horde and Beast, which seems weird. The game's matchmaking tried to match us into six different Horde matches even though it says none is being played—but it didn't join us to any. No big worry. The game's not out yet in many places (Note: I found a public match for Beast Mode yesterday.)
Gears of War 3 will officially be out for Xbox 360 at midnight, September 20, in North America, Europe and Australia.