Google's social network, orkut, doesn't need an invitation anymore. You can sign in using your Google Account.
The invitation was one of the reasons behind orkut's failure to compete with MySpace. Now that Facebook is also public, the competition will start to become interesting.
orkut has around 30 million users, and more than 60% of its users are from Brazil. It was launched in 2004, the same year Google unveiled Gmail.
Update: this page should let you join orkut. Unfortunately, the link doesn't work for everyone.