I learned about talkers in a 'how to use/things to do on the internet' book, and hung out on one of those for about a year before my high school got internet access and I noticed an interesting-looking connection someone had when I did a w. So I telnetted to that address and discovered MU*.
Initially I tried it out because it reminded me of what I already liked, but it was Star Trek based rather than being just sort of a random hang-out, and the differences between it and what I was used to were interesting. And in all honesty, two of the things that drew me in were the same things that had with the talkers: 1) despite a fair bit of social anxiety, I like being around people, and these let me do it under my own terms -- whenever I wanted, easy to leave, not necessarily with physical proximity, and 2) people liked me. I'd never been a particularly popular kid, and in middle school I was practically a pariah, so it was kind of mind-blowing to suddenly be someone people thought was cool and funny and appealing to hang out with.
But I switched over because I liked RP, which was new to me then (beyond playing make-believe as a younger kid, which I had loved). I liked the idea that you could come up with your own character to do things in this fictional world, and also still talk to and hang out with people as yourself. I was a theatre kid, and I liked the sort of on-stage/off-stage effect.
Having a place where people liked me when I was being myself is probably what kept me in at the beginning, because the RP itself wasn't really that good for a while. But I liked writing, and I always particularly liked dialogue and characterization, and once I got to a place where things, as @Arkandel said, click, that was probably it. My own character surprising me with a reaction is definitely one of those feelings, and relatedly, when I can't figure out why s/he did it until days or weeks later when suddenly it's entirely clear and makes complete sense. Actually, all three of his examples, definitely.
I like the persistence in changes in characters and world, and I like the ongoing nature. I like the lack of graphics -- I've tried RPing on MMOs and SL, but if you pose throwing Bob down the bar and I can see both of you just standing there, I have no immersion. In text, that's not an issue. And I love words. Oh, and speaking of immersion, I like being able to feel for my characters, and other characters, and I've never really found that anywhere else.
Also, the real-time, online, collaborative creativity aspect is fascinating enough I made it my focus in grad school, so there's that.
...these days I'm also appreciating the fact that it doesn't have to be as ephemeral as something like TT or LARP. I have logs that are old enough to vote, now, that I can still go back and read and really get into the stories again. That's kind of awesome. I wish I'd logged everything from the start.
