No warnings: you beg, you banned.
Begging is way too common both in bitcoin forums and in some online games, and it should definitely be stopped, without warnings.
Anything else shouldn'd be censored imho: censorship is a bad thing. If we "censor" anything, it's just because we have to prevent spam from happening, or the chat becomes useless. So, as long as you aren't spamming (begging included in spamming), that's fine.
Advertisements are the only exception, for obvious reasons.
Can't we just implement an easy to use ignore filter? One-click ignore & leave it up to the users. Self-censorship doesn't hold the same kind of risks of centralized censorship.
There might even be people who enjoy throwing a few coins at the beggars.