One of the easiest ways of establishing pseudonymity is to use public key cryptography. Publishing a public key allows messages to be sent confidentially to pseudonymous parties. Of course, a working address is still required to allow the message, however confidential, to reach its intended, if pseudononymous, receipient. Because only the holder of the private key (ie, the one matching the public key used to encrypt the message) can decrypt the message, it cannot go astray and be read by anyone else.
Pseudonymous remailers, called "nym servers", have been set up for the purpose. They take messages addressed to the pseudonym and send them to the pseudonym's 'real' email address, while forwarding messages addressed to others as though from pseudonym's address on the server. Unlike truly anonymous email, replies can be sent to the pseudonymous sender, and the pseudonyms can establish digital reputations.
Remailers which allow such nym identities have different 'exposure potential' than do true anonymous remailers. Whenever there is provision for reply to a pseudonyomous posting, some record must be maintained of the correspondence between the nym email@example.com and the real name John_Smith@bar.com. Even if that list is protected cryptographically, located in another jurisdiction, and/or concealed by a chain of nymservers, it is always possible that legal action (or brute force or sloppy system management or devious hacking) can expose the underlying address of John Smith.
It is precisely this which caused J Helsingus to take down the penet.fi nym server. He was sued by Scientologists for the identity of someone (or ones) who had posted material they didn't want posted (copyright violation was claimed), and the Finnish courts held that he would have to disclose actual email identities. He chose to close the service and destroy all his records instead.