Address Book has had a field to store a nickname since I don't know when (use Card -> Add Field -> Nickname to add the field to a card you're editing), but in Leopard, you can finally actually put that field to good use. First, as noted in this hint, Mail will now recognize and use the nickname field.

Second, In iChat, select View » Buddy Names » Use Short Names, and iChat will use the nicknames in the Buddy List. (Note that if you do this and you're storing iChat transcripts, the transcripts are stored according to the name listed in the buddy list window.)