On this style of bulletin board, Mods and/or Admin cannot read your private messages. They are, however, able to see how many messages users have in their Inbox and Sent Mail (see attachment). The only way they can read your Private Messages is by changing your password.
Edit: People are saying Admin can, I can't see it in Admin's options?
This is an interesting topic. I'm pretty sure it's illegal to read PMs unless either the sender or the recipient has given permission, either express or implied - perhaps via something in the T's and C's. I think it comes under the same legal umbrella as a sysadmin reading e-mail between people on his system.