Well, I'll throw out some answers and hope for Cunningham's law to kick in...
It depends on the mode that you are in:
For Realtime manual mode, I believe you can only host one table.
For Realtime automatic mode, I don't believe there is a limit other than how fast you can click. When any one table has enough players to start, you will automatically leave any other tables you are waiting in.
For Turn-based, the system imposes a fairly small limit to start with -- something like being able to be in 3 simultaneous games. But, for each game that is completed, that limit increases by 1. With that there are accounts on BGA that have a couple of hundred simultaneous turn-based games active.