I don't know what the record is, but I was in a tournament and one guy had over 1000.
What's the record for online games at one time?

You would have to ask him, bjonil60. I guess it wasn't easy, because he resigned a lot of them all at once, now he has just 58 going.

One thing that is mildly irritating about this fellow is that when I got the winning position in my game against him I was around 1390 or so and he was just over 1700, so I was excited about the game and the potential jump in my ratings.
Since then he has lost dozens of games to time, his rating has dropped down into the 1500s, but he hasn't given up on my game although it is hopeless for him. So now I don't get much of a boost if I win
In the grand scheme of things there are bigger things to worry about.
One of my twenty or so opponents at the moment on online chess has about 260 games in progress. What's the record?