It seems that its now possible to get a gMail account without first requiring an invitation or SMS code.
Follow the link at the gMail frontpage to see if its permitted for your particular country. I am in Australia so can only confirm that Australians, at least, can now sign up directly, which may please those who were anxious about needing to give their email address to a stranger such as myself in order to get an invite.
Once you have a gMail account, you can also access an online Calendar, and Googlepages. These may or not be of use to you, but I thought them worth mentioning.