Usually about a dozen.
How many online chess games do you have going?

not sure at the moment, I generally run about 50 at a time, though often ill just let them die down till theres very few left
I had up to 40 going but now I only have 2. Trying to finish up these set of games, which brings me to 100, and see how I fared with my first 100 games and where I ended up in rating. Then I'll probably only do a dozen at a time or so. I had a lot going earlier so I could get to play a lot of higher rated players while my rating was high from an early winning streak I had when I started here (was 1804). I thought I'd get knocked back down in the ratings from it, but surprisingly I've held my rating pretty much around that! So that shocked and delighted me.

I have 5, one of which is essentially over, so it doesn't really count...
Check out jcasey, he has around 200!

23 - The most I've had on this site at one time. I don't think I will be starting any new games for awhile.

I have 70+ now which is too much for me. 40 or so is more comfortable. I know a strong player here with 400+ though, he's a machine!

16 and I'm swamped.
I've played people who had 300+ going at at time. Those people amaze me.
Poor poor poor bird!

I usually run about 50 at a time. I think I am going to drop down to about twenty soon because my rating has been stagnant for the past year. Hoping more time spent on moves will increase my rating...
I have 27, which is the most ever for me.