My favourite RP moment has got to be one that was almost entirely Player Driven. I remember it quite clearly. My character followed someone else (a rich mafia princess, is essentially what she amounted to) to a bar. She went in and sat beside her, and they ended up talking to each other. They drink and get a bit tipsy each, and it ends up with them kissing each other then the Mafia Princess inviting my character to her room to sleep (only sleep. Separate beds). 

To this day, no other piece of character interaction has felt as natural as that one. The fact that they were two strangers who peaked each other's curiosity, and acted upon that, makes it easily my favourite moment. We hadn't talked about anything like that beforehand. We just... wrote, and things happened. 

[@Darcs] (I saw her write a bit in here at some point) will know what I'm talking about :P