Can I sign up without the invitation code? Or without a mobile phone?
You need to receive and enter a special invitation code in order to create an account. Currently, we are only sending these codes as text messages to mobile phones. So you will need to have a mobile phone with text message capabilities (most phones have this) and the invitation code itself.

One of the reasons we are offering this new way to sign up for Gmail is to help protect our users and combat abuse. Spam and abuse protection are two things we take very seriously, and our users have been very happy with the small amount of spam they've received in their Gmail accounts. We take many measures to ensure that spammers have a difficult time sending their spam messages, getting these messages delivered, or even obtaining a Gmail account (spammers will often use many different accounts to send spam). Sending invitation codes to mobile phones via SMS is one way to address this, as the number of accounts per phone number can be limited.

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.