As I found another one of my questions closed by a moderator, it lead me to wonder how powerful moderators are. I know they can close questions as "duplicates" and "off topic", but can they throw someone off the site? Thanks!
This answer on Meta Stackoverflow (the master policy site and guidelines for the network) should answer your question as to the things moderators can do.
To answer your question directly, yes, moderators can suspend someone for breaking the rules, being repeatedly rude, etc. But suspensions are monitored by the Stack Exchange, Inc staff, so it's very difficult for a moderator to do it wrongly and not have it come to someone’s attention.