If you want to use some Google services like Google+, Drive, Calendadario, Keep or Google Play you can do no see forced to use a Gmail account.
It’s interesting to notice That the only Google service That Uses the new form and lets you use your own email address is Google Drive. You just click “I prefer to use my current email address” and skip creating a Gmail account. Here’s the link to this version of the form: https://accounts.google.com/SignUpWithoutGmail.
You can also use URLs : like: https://accounts.google.com/NewAccount?service=cl
Note: You can also use your own e-mail to the backup and sync Chrome
Update: This option is no longer available: 2018
This recipe does not work anymore.
If you can use Google services (except Gmail on desktop) with any type of mail. They only need to register from their smartphone.