As the manager of a vulnerability research team, I almost always organise my team's meetings to start at 13:37. It's become customary for us to refer to it as "leet o'clock".
Edit: the time changed to 13:38 just before I hit submit :(
Missed leet time by one minute though...
In our working group (astrophysics) leet o clock is the traditional time for cake.
Also, how long do the meetings last? If you're serious, it's a nice gimmick but terrible for actual time management.
There's another one I call "Razor o'clock" at 7:11 pm, i.e., 19:11.