My record is 16 tables .
Before anyone says GTFOOH, I'll explain. I played 16 penny tables at once on PS around that 10 billionth hand celebration in hopes of getting the 100k. It didn't happen . What's not so funny about it is that actually the 100k if I recall correctly was given to a penny table. Needless to say I was going nuts on 16 tables for those ~45 minutes I played them, about a few hands in I was just about folding every hand, I decided to play only AA, KK, QQ and AK lol. It was crazy man. As soon as the 10 B hand was dealt I was out as fast as humanly possible.
For the most when I play tourneys I only do one at a time, occasionally I'll play 2. On cash games those few times I play them, I'll play 2 at least and sometimes 3, recently I tried 4 at $50MAX but I won't do it again, I really played poorly . Didn't lose much because I played super tight, but for me at least there isn't much to gain by doing it.
I read about the guy who plays 24 sitngos at once, don't know how you can do that, for sure not on a 17" screen.