Currently you need a gmail invite to your email id by someone to open a new gmail account. Now US users can get gmail invites via SMS on their mobile phones.
This new way to sign up for Gmail is to help protect users and combat spam and abuse. Just go to the Gmail mobile invitation code page and enter your mobile phone number. You will get a text message with an invitation code to create your account. You will need to have a mobile phone with text message capabilities. Currently this promotion in the United States only.
If your mobile number privacy is a concern, remember Google will store each phone number to make sure it is used to create no more than 10 accounts. If you want to open an account a different way, you may want to ask a friend with a mobile phone to receive an invitation code for you or to ask someone you know who already has a Gmail account to email you an invitation.