Mods can ban you from communities, cancel any of your posts, delete any of your comments. That's about it.

The trouble is that people are unfairly banned from subs they have followed and contributed to for years and there is no appeal other than begging the guy who just maliciously kicked you out

That's not counting mods who are also admins and mods who are good friends with an admin. You can get a site wide ban for saying the wrong thing in front of one of them