I've always been intrigued by this sort of idea, and have even made a character or two myself that had such limitations placed upon them. Recently, during the long dark night between patches, I got bored with my mindless and aimless farming and decided to create a new alt. I decided that this character would be a Draenei warrior, but that he would only fight unarmed, with a staff or with a throwing weapon. I also decided that he could only wear cloth or leather items. I suppose my idea was based somewhat on a sketchy notion of some kind of fighting monk.
I've always found the idea of a staff-wielding warrior kind of humorous, at least in WoW, and I even had Slavedriver's Cane on my warrior alt for awhile. As you might imagine, making another warrior that exclusively uses staves was appealing to me. The real draw of this type of gameplay, of course, is that it makes you rethink the entire way you approach leveling up. In essence, it's like creating your own character class. You need to think about what type of gear, professions and talents you choose in order to be as successful as possible given the new limitations you've imposed on yourself. For people that have been playing this game for several years now and have alts of every class, it's this type of thing that can keep one interested in WoW while waiting for the next patch (even if we don't have much longer to wait for the next one).
Have you ever done anything like this? Do you have any ideas for other interesting self-imposed limitations?