The most prominent way to bring your fantastic, awesome, uber character back down to earth is by giving him or her some flaws. These flaws shouldn't be as simple as "Bob is afraid of cats." The flaw has to be meaningful and should be part of the overall characterization. For example, "Bob is afraid of cats, because his parents were killed by a tauren druid." This allows the flaw to be part of your character's story, instead of just being a random quirk that shows up in emotes.
The most famous example of a character flaw is probably Oedipus's hubris. This overwhelming pride eventually led to his downfall, and was a major motivating factor throughout his entire story. But that's some pretty old fiction. If we're looking to more recent fiction for inspiration, I would check out Dr. Gregory House.
Dr. House is obviously a pretty awesome character. He's smart, charming, attractive, and incredibly intelligent. However, his pride and cynicism drives Dr. House toward amazing mistakes. His pride keeps him from professing his love for Cuddy. (Come on, we all know they should be an item by now.) His cynicism leaves him in constant conflict with his friends and allies.
This kind of character flaw keeps House from becoming a simple medical procedural show. Instead, the dynamics and conflicts created by House's flaws create a series of plots. Will House find love? Will he ever become a good person? These inner conflicts are part of House's charm, as the audience constantly roots for House to "grow up."
If we bring this example into our roleplay, then we'll be able to create far more compelling characters. Perhaps you could play a paladin who is so enamored of Right versus Wrong that he refuses to see any shades of gray. Work with your fellow players to create a situation with them that forces the paladin to operate inside some morally ambiguous areas. The character flaw will set up dynamic tension as the plot moves forward, giving the paladin an opportunity to either grow as a character . . . or deep-six the entire group around him or her.
That's just one example, though. Perhaps one could play a noble warrior, who is sworn to an old code of honor. Women are to be treated with respect and protected at all costs. How would such a character interact with a deadly female rogue, who is more than capable of killing most enemies in her path? The warrior would probably be forced to struggle, either eventually changing their own code of honor or dealing with the juxtaposition of his outdated ideals and this more-than-capable woman.
Many roleplayers incorporate flaws like alcoholism, sadism, and greed into their characters. I'm not entirely sure how those became the cool characters traits, but they frequently show up inside FlagRSP as I wander around WoW's many Goldshires. I think there are a lot of opportunities to be had there, but I'd still try and go outside the box a little more.
Other available realistic touches, however, involve more subtle character quirks. Food preferences and fashion taste are two such examples. I've seen many vegetarian druids, for example, and that idea always rings very true to me. Heck, druids are only a single button away from being animals themselves, so it would make sense that the followers of Elune might have some issue with meat-eating. As for fashion taste, it's always interesting to me how many roleplayers describe their characters in terms of "well cared-for armor" versus "battle-scarred and dented armor." While you're probably not wearing your very best plate armor in a pub, it's still a subtle touch that conveys a better understanding of a character.
Emotes, of course, are very useful to getting character information across to other roleplayers. As I've mentioned before, however, you have to be pretty careful with emotes. They can be a great tool for character description, but it's far too easy to trip into the realm of over-sharing. Try to stick to things that other characters could easily perceive. If another character couldn't tell a fact by looking at you, then it probably doesn't belong in an emote.
What other things do you do to make your character more realistic? Do you try and describe your character's features? Do you publicly display any character quirks? Let me know in the comments. The best way for us all to advance our art is to share our techniques, and I'm eager to hear what you have to say.