Yes, you can get a virus from social media sites. The Wall Street Journal reported that less than 1% of Facebook's 150 million users have become infected with malware using the site and only a ""negligible amount"" of MySpace's users have been infected with malware. Cyber thieves follow the crowds and with the rapid growth in social networks and social media sites, criminals are looking to exploit your sense of security in being part of a members-only community. For example, it was reported that hackers created fake celebrity profiles that when clicked on, downloaded malware onto the computer. Hackers then mined infected computers for logins and passwords to financial sites. Infected computers can also be used to send out spam emails, propagating the malware among your friends. You should exercise the same precautions you use with email messages and pop-ups (See, How do I prevent spyware and malware?)
MySpace, Facebook and Twitter, to name a few, employ teams that investigate malware threats, phishing attacks and spam on the sites. The companies also have automated processes that monitor for and delete phony accounts, malicious messages and links.
For more information on how to stay safe, see What is the best way to prevent phishing?