Coming from a MUD stint myself, I can safely say that the right MUD's and MUSH'es have so deep and complete RP that it feels completely different trying out a MMOG again. MMOG's as a medium are simply much worse at stimulating RP than a MUD or MUSH. They on the other hand, are as close to pen and paper RP as you can get, so of course they will be the 'ultimate' RP experience possible in an online form. At least that's what I experienced. The closer a MMOG is to a MUD/pen and paper RP, the better it is. Ability to do whatever your char wants to do, ability to affect and move the storyline, real GM's who make stories around you and others, and NO OOC'ers at all. That would be wonderful in any game. MUD's/MUSH'es are where this is at. Ah, and of course Live Action or Pen and Paper RP.
As for MMOG's that provide the best tools and setting for RP.. Well. EVE doesn't provide any tools and lacks avatars, but it is a great setting to RP in for sure. SoR right now lacks RP'ers and the developers are not taking the world anywhere, nor do you have any influence over the storyline. Roma Victor I haven't tried, but to me it looks like Adellion or Fallen Earth are the only upcoming stars on the MMOG horizon. Fallen Earth have designers who come from MUD's too. These two are hardly mainstream MMOG's, nor will they grow big. EVE however is pretty big and mainstream, which is impressive. They've come far with their vision.
I hope it's possible to RP meaningfully in EVE, create stories and so, but I am a little sceptical about that aspect, with or without avatars. However, as Mecha says, there's a lot of RP in politics, strategy, etc. in EVE. That has huge potential. And as Zhiroc says, behind all that, it's a race to gain more money so you can buy more, equip more pilots, and fight more. That is at the core of corporation and alliance gameplay in EVE. Gain skillpoints and earn ISK, to be able to earn more ISK and to fight. But then again, isn't that the formula for most if not all MMOG's? EVE is unique in that it provides what Mecha describes at least, and with RP you can make it even better. However, RP takes the second seat, or is 'tacked onto' this structure, it doesn't feel natural, integrated into the game right now. Probably because the game lacks tools. These will come with the avatars hopefully.