I can't speak for other RP servers, but I play on Steamwheedle Cartel (US), and I like to call us the RP server that wasn't. The "RP" denotation in our case is kind of vestigial at this point.
Also, on a bit of reflection, since this is a question 100% aimed at those that play on a PvP server, wouldn't this topic be better served in the PvP forums?