Google Operating system blog reports that after 3 years of invitation only access, GMail is opened for public sign up. The service is still strictly in beta, even though it’s been around since 2004. GMail started with invitation only sign up in April 2004. Later in 2005, it allowed anyone in the US to get an invite by having an invitation code sent via SMS to their mobile phone. Now you can sign up GMail with out invitation or invitation code at http://mail.google.com/mail/signup.

From initial launch they took 3 years to open for public and how long they take to move out of beta(public beta)?

Update:
From
BBC news

An earlier version of this story - based on a Google statement to the BBC - had reported that Gmail was now freely available around the world; however Google has now withdrawn this statement.

Now users can now freely sign up to Gmail in across Europe, the Middle East and Africa, as well as in Brazil, Australia, Russia and Japan. So in US, it’s still by invitation only.