I've been in as many as 14, I think, though not all of them were active... right now I have 11 games, 6 of which are active:
Dark Nova 4 (active)
Fantasy Empires - First Game (declared over but never deleted from PBW)
Highliner Mod Shakedown (active)
Invasion! Official 0.41 (still waiting for more players, c'mon and join so my monster race can eat your ships!
)
Junkyard 24XX: Battlegrounds (eliminated from game but still hosting)
Puke's Mail Order Monsters II (active)
PvK's Proportions Game #2 (active)
RTV Tudran Game (active)
Star Control (not started yet - anyone wanna join as a SC race? we have about 6 players right now!
)
Star Trek: Quadrants of Conflict (active)
The Pointer Mod Game 2 (c'mon, START this game, I wanna play the mod!
)