When Gmail originally launched on April 1, 2004, it was entirely an invite-only service. You could only get an account if someone you knew already had one and sent you an invitation. At one point, Gmail invites were even selling on eBay for well over $250 a pop.
In the middle of 2005, the system opened more widely, when Google allowed anyone in the US to get an invite by having an invitation code sent via SMS to their mobile phone.
It now appears to be officially a public beta, which means you don’t need a Gmail invite or SMS code to gain access to your own Gmail account. If you want to sign up for a Gmail account, go here.
Postscript: Google Officially Opens Gmail To World, with Google’s statement.