I've never seen anything harder than V10 at the gym, but I'm sure they exist outside.

I think I've seen a V11 at the place where I climb, but it was only after they'd had someone very high-powered guest-setting.

Outside, the current hardest problems in existence are V14s and V15s, with a very few possible V16s. But only a tiny handful of people in the world climb at that level.

ETA: thank you for pitching in!