Game I had last night went into 4 OT's.  Box Score

The sim's  SG hit a game tying 2 with 1 second left in regulation, then he makes a free throw to tie it with 6 seconds in the first OT, but missed the second which probably would've won the game.  Then in the 3rd OT i hit a game tying jumper with 9 seconds, before pulling away in the 4th OT

whats the most you've seen?

I've seen 4 before, but I'm not sure I've ever seen 5 or more.

I had a 4 OT game in which the other team (a huge underdog) hit 2 half-court shots to keep us playing and finally beat us when we had no one left to hardly play. I thought it was strange, was a bit upset so I looked across the rest of Allen D3 that day and there were 3 - 4OT games and 2 - 3OT games that night. (which I thought was really strange). I think every game was won by the dog.
In Vegas you can see long runs of random numbers, (10 straight red, a dozen or more evens, seven rolled 5 straight times)....(I once saw a guy roll an 8, six straight times)... so it can happen.... but there are things in HD that don't happen just by the RNG.
Crooked refs have a lot to do with it I think