There's a growing perception that actual roleplaying is difficult, perhaps impossible, in MMOs. I play World of Warcraft on an RP server, and I'm here to tell you that it's entirely possible. I won't claim to be a perfect authority, but I RP my way through the whole game, pretty nearly. Here're some guidelines for roleplaying in WoW, from my own experience.
I'm going to go at this in three parts: Background, Mechanics of RP, and Plot. All of this, really, is focussed on increasing immersion, and not breaking it.
Background
1. Have your character's background worked out. It doesn't matter what it is - I'd argue that it's almost better to have them be a farmer's son than the missing heir to the throne of Durotar, but it's very much a case of whatever floats your boat. Just know what it is, and stick to it.
2. Very few people are going to hang around while your character tells them the background. Come up with some way in which the background is evident in your character's behaviour, if it's important to you, and if not, don't worry about it. For example, my main on Argent Dawn, a Forsaken who calls himself Wormson, was an arrogant know-it-all when he was alive. Seeing this as the reason for his death, he now asks questions all the time. Another Forsaken character in the guild has a history involving a lot of fire magic, and also being a farmer - and memory problems. Because of this, most of what he says in conversation deals with fire and sheep - sometimes sheep on fire.
3. WoW provides you with incredible amounts of information about the world and the races in it. Know your own race's background reasonably well, unless you're playing a librarian, teacher, or the like - in which case, make sure to know more than most people. If you don't know much, and don't have the time to read up on it, make sure that's reflected in your character. "Oh, so that's where orcs come from!" is a perfectly valid response for a non-orc arriving in Outland, for instance, but not knowing that orcs come from another world, while playing an orc, takes some explanation.
4. Be consistent. Nothing is going to undermine other people's experience of your character more than her being a princess one day and a milkmaid the next, to take an extreme example, or referring to her mother when she's previously told people she's an orphan. Mistakes happen, of course, and if you want, you can work it into the story - "Yes, I meant my foster mother," or "I have no recollection of that conversation. I must have been possessed!". Otherwise, just whisper to the other players involved that it was a mistake, and ask them to ignore it.
Mechanics of RP
5. Everything in the /s and /yell channels is in character. Your character is saying these things. Therefore, do not say "lol", or "
". While I've heard people say "lol" in real life, nobody in Azeroth knows what it means, and I don't know anyone who can pronounce "
". If you want to communicate an in-character laugh, there's /laugh, /giggle, and so on, also /grin, /smile and the good old emote command: "/me laughs".
6. Ignore the non-RP aspects of the world. If someone gets disconnected, don't try to roleplay around it, just wait for them to re-appear. And unless you've got a good explanation for why you're standing there talking to someone without bits dropping off "Yeah, I died three times trying to get in there" is not a useful sentence.
7. Walk occasionally, at least in towns. The NPCs don't run much, and anyone who runs everywhere doesn't look particularly in-character. Walking indicates to other people that you're interested in roleplaying, too - nobody walks when they're questing, of course, or on a mission, or whatever.
8. Don't power-emote. That is, don't force the outcome of an action on another player. "Lemuel punches Arkas, knocking him to the ground" isn't fair to Arkas' player. "Lemuel throws a punch at Arkas without warning" is fine, though - it allows responses from "Arkas is knocked to the ground," to "Arkas dodges, and takes a few steps back, looking shocked" to "Arkas is winded by the punch, but aims a kick back at Lemuel".
Plot
9. It can be hard to roleplay in a world where nothing changes except the other players. Even if you've roleplayed your way through a huge plot, with lots of discussion, events, and action leading to the death of Staghelm, he'll be back within hours. There are two ways around this - the first is to assume that there's an explanation in-game for it. "He's an imposter!", or "The one we killed must have been an illusion" both work. The second is to work with player characters as opponents.
9. "Player characters as opponents" needs some expansion. What I'm talking about is when someone develops a character effectively as an NPC, plotting against other players, trying to bring about the downfall of player guilds, ousting the current Guildmaster, and so on. An awful lot of this can happen, effectively, in conversation, and you can use duels for when there's an actual fight. It requires some cooperation between the players, but that's not hard to manage.