There are 12 "servers" at the moment (divided among some regions, I think 6 for europe). But each server can host several realms, so I'm not quite sure how many realms are there, but at the very least 12 (probably 30 or more, though). A server can handle up to around 200 players (I don't know the exact number, the CPU is the limit).

I only notice about 50 people at once in most servers. When there is one big behemoth at least twice the size of the one in 2nd in the leaderboard, most people simply RQ.