They are spam magnets.
rfc822 (section 6.3), and its proposed replacement, rfc2822 require postmaster (and postmaster@domain) to be a valid, non case-sensitive address, so technically, if you send or receive mail, you should have this as a valid, and working address.
In general, not having one won't cause you too many problems, but it could get your domain listed in rfc-ignorant.org. Also, Sourceforge checks to see if you have a valid postmaster@ address before letting you subscribe to mailing lists there.
We do highly suggest having a valid postmaster address. Whether abuse@ is required for all domains is a topic of some debate. Generally, someone that has an abuse situation would probably contact our abuse box directly. It still might be a good idea to keep this address valid as well, however.
Also relevant is rfc 2142.