debate a'brewin' about identity online. Facebook is opposed to people using anything other than their real names - primarily, it would seem, to combat cyber bullying. Google followed suit when they launched their Google Plus service - but they took a lot of heat for not letting people use pseudonyms (nicknames).
Mathew Ingram at GigaOm has a good post on Google's position on real names.
Fred Wilson has staked his position. As has the Electronic Frontier Foundation. There's more coverage on this listed below under "Related articles".
I don't think there's one answer that suits the internet as a whole. There are cases where anonymity is needed (e.g. political discourse in repressive countries). And I do (mostly) agree that real names clean up most of the bullying, nasty, and spammy comments online. But it doesn't prevent all bad behavior.
One part of this debate that some folks might be missing is that pseudonymity is not the same as anonymity. Using a nickname to create a different persona online is a fun and expressive way to participate in social media (sharing, blogging, twittering, etc). But it's not the same as anonymity.
I choose to use my real name in most places online. Many of my friends use pseudonyms (but I still know who they are; they're not trying to hide their true identity). Bottom line: I think it's a personal choice.