FlagRSP2 and MyRolePlay both give you a space to write things like your character's first or last names, a character title (such as "Priestess of the Dark" or "Wacky Troublemaker"), as well as some description about what your character looks like; and of course they both enable you to see the information other people have written about their characters too. Both have "roleplaying flags," which can tell other people whether you are a "casual" or "fulltime" roleplayer, as well as whether you are in or out of character at any given moment.
FlagRSP2 has a cleaner, more intuitive interface, in my opinion, and it has nice little popup windows for character information which can appear whenever you mouseover or target someone. MyRolePlay only has a popup button which you must click on to see other characters' information, but it also has two separate spaces for physical descriptions and story backgrounds, which FlagRSP2 users sometimes mix up together. MyRolePlay also uses less computer resources on my system, and keeps things running a bit smoother. I often switch between the two since I can't really decide which is best.
A few notes on using either of these addons well: As the wonderful comic Hammer of Grammar showcased last month, it can be tempting to use a bit too much melodrama when writing character descriptions. As we've said here on WoW Insider, it's important for characters to stay relatively normal, and to be drawn from real life experiences, unless the character's whole purpose is to be a silly farce of some sort. When writing FlagRSP2 or MyRolePlay descriptions, stay away from cliches such as "half-demon," "deep sadness," and "a patch over one eye." In fact, you might even consider limiting your description to just a paragraph or two -- some players do very well with just a single sentence, such as "He scowls at you."
For my own characters, I usually assume that people don't have a lot of time to read my descriptions, so I put the type of things they would notice first at the very beginning, gradually going into more and more detail as the description goes on. I try to keep the total description under 300 words or so, and I never put background story there -- that's something I save for people who take the time to get to know my characters by talking with them.