Xbox Live has been up, but the Xbox Live site and Xbox.com had been up and down in the past few weeks, which could be Microsoft's reaction to hacking attempts.
However, LulzSec has announced on its Twitter feed that they were going to target Facebook and Social Networking accounts, gloating, "Envelope yourself in the sickening realization that you secretly love ***** someone's Facebook life beyond repair."
Microsoft has been mum about any breach so far, and there have been no reports of accounts being hijacked as of yet.
"This group appears to have posted a list of thousands of potential email addresses and passwords, and encouraged users to try them across various online sites like Xbox Live in the event one of the users happens to use the same password and email address combination. At this time we do not have any evidence Xbox Live has been compromised. However we take the security of our service seriously and work on an ongoing basis to improve it against evolving threats.": Microsoft has released a statement, which states that Xbox Live was not compromised to the best of Microsoft's knowledge, and the logins/passwords were released at random, with people encouraged to try said information on services like Xbox Live (among others).