Well, my answer would be much different if you hadn't restricted this to RP. I haven't RPed much in MUDs, so I'll have to cheat and say that I got the most pleasure from my character in the old AOL "red dragon inn" and related chatrooms. These were not exactly MUDs, but were extremely close to being very basic stand-in-a-room-and-emote-actions-and-chat MUD, so I'll count them.
Of course, back then I was like, 12 years old! So forgive me for being a (long ago) former AOL idiot!  Anyway, the fun thing about Red Dragon Inn chatrooms was that anything went: just enclose your actions in :: ::, and you can do anything at all, no limit. People would have silly "fights" which rapidly got to be ridiculous, but it was good fun. Looking back in retrospect, I realize now a lot of the purpose of those chatrooms was probably for people to hook up for the AOL version of mudsex... which was quite over my head at the time (fortunately)
Edit: Oops, I misread you and didn't realize you wanted us to describe the CHARACTER itself. Back then I RP'ed as Magus from Chrono Trigger, a badass wizard. Yeah, not very original (well, not original at ALL), but oh well, sue me.  I also sometimes RP'ed as Galuf from FF5, a wizened and eccentric warrior type.
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