25
Most Games

I actually only have 3 going right now, and I'm so busy I hardly have time for those. When I actually have spare time, though, I still only like to have around 5-7 games. I tend to take a while to move, and I get sloppy if I'm playing more.
I really don't see the point in playing many correspondence games at once. It's better if I can focus on making the best move on one game for the time I'm given; 3 days at the least is a lot of time! Plus, live chess can be much more fun than the CC here on the site.
On top of that, I think getting my CC rating up in USCF would probably be better....
I do have two games though going on right now on the chess.com CC server.
Put down how many games you have on now:
104