15/10. With less than 15 minutes I totally panic
What game mode/time is most popular?

A lot of FIDE events are played at 40 moves in 90 minutes and then 30 minutes till game end with a 30 second increment per move starting at move 1. I think the minimum time controls in USCF events are 30 moves in 30 minutes or slower.

For internet games, I'd guess either 3/0 or 5/0, both of which are very popular.
I haven't been playing much recently, so maybe 2/1 is becoming popular? I wouldn't know.
me, I always played 10mine games.