From what I've seen on various sites, Lord Adraas seems to be one of the heaviest RP servers. It's the one I play on, and the guild I am in (Crimson Twilight) focus heavily on RP. We have constant RP events, and the guild leader is heavily dedicated to it.
It's a lot of fun, and if you need a partner or few to run with and RP with, we are always up for it. We are Emp side, but I plan on making a Repub branch if I can.