People from Digg report that Gmail doesn't require invitations and that you can get an account by simply going to this page. It doesn't work for me, and it seems that it doesn't work in Europe.
At the moment, Gmail is officially a public beta in Australia, New Zealand and Japan. The day when Gmail will be available to everyone is very close.
Can you create an account? Do you see this on Gmail's homepage?
Update: It seems that Gmail is available without invitation in Egypt.