Gmail, the webmail service created by Google back in April 2004 has come a long ways since its launch. Although the public launch was sometime in 2007, there was an invite system where people can sign up. Officially Google does not offer any option to find out when you created your Google (or Gmail) account. But with the release of new migration tool for Google+ which allows users to change from one Google account to another (Google Apps), you can now find the creation date of your Gmail account.
To find the creation date, open this Google Takeout service- http://www.google.com/takeout.
In the Google takeout service, click on the link, Transfer your Google+ connections to another account. This will prompt you to enter your Gmail password and once confirmed, it will open the migration tool. Here you will be able to see the Gmail account creation date under the box “Move data out of this account”
This will work for all Gmail accounts as well as Google Apps accounts. Other work around is to check the first email which you received in your inbox which might not be the correct one as you might have deleted many emails.
Thanks to Caschy for this tip.