If you have an AOL, yahoo, or other preferred email address you are still able to obtain a Google Account without having to sign up for Gmail.

Google Account

Associating your current email with a Google Account provides you access to all of the Google products except for Gmail. This includes Google Drive, Google Docs, YouTube, and more.

No Gmail

If you do not want Gmail go to https://accounts.google.com/signupwithoutgmail and sign up with your current email address. When signing into Google products such as Google Drive you would type in your current email address as your username.