At one time, i had to set my profile to "Not Available for Challenges" and concentrate on the on-going ones. HOnestly, it is not advisable to be on too many games 'cos you loose concentration and your game plot.
How many online chess games do you play simultaneously?

I lost many games then that i know i should have won and now i know this guy who is on 1070 games!!!! - that's just crazy. He is good cos he is high rating but he's lost but games to me due to minor errors (he should have won me in both- in my opinion).
So avoid too many games at any one time if you can.
I'd say 20 - 30 is just adequate (but depending on your skills and all....)

I've played as many as 40 and as low as 8 or so and haven't noticed much of a difference. The big deal with for me is when I try to play several games during work and end up making blunders because I'm playing chess on one screen and programming on another.
I guess my point is it really matters how much concentration you can give to any particular game. Not the number of games you're playing.

its too boring unless i have around 100. My game suffers a little but I just cant enuff chess. This is an awesome site with some really good players. Try the tactics trainer!

To keep busy , I need about 40 - 50 games ,most of them are 3 day time limit so I have the option to skip a day . I feel a little rushed sometimes and thought before that I do better with less games , but I get bored when my oponent doesn't move fast enough and I start new games again .
At one time i got so choked up with these games that it took almost 5-6 hours to submit just one move on each board of 89 games so i can run off before another person submitts their move and i have to stay on longer 'cos i had other stuff to do.