All domains need standard mailboxes (see RFC-2142) to receive e-mail for administrative and technical purposes. If your domain doesn't have them set up it can cost you a lot, especially since new domain registration rules by ICANN can cost you your domain if you can't receive notices at those addresses. Here's a list of the addresses you need to have set up and what they're generally used for:
There are other mailboxes defined in RFC-2142, but they aren't mandatory and you probably won't be running services they'd be used for. One easy way of handling these is to forward all of them, along with root, to your own mailbox. That way all the critical e-mail ends up on one place and you're checking it regularly anyway. If you've got a larger shop with several people managing your network and systems, you'll want to forward those addresses to the person/people responsible for that area of operations.