Not is not uncommon for a A/R service to not like free email like yahoo and gmail address. If you are serious about creating a list just make a dummy address like support@yourdomain.com. Create it in your CPanel and forward the address to your free one that you like. Then you can use that new email with aweber and not have an issue.

I've seen some aWeber + Gmail?

Aweber allows free email (gmail, yahoo etc). They just don't recommend using them. You can still create a campaign using your free email address.

V

With so many people spamming and the laws that are being put in place getting tougher and tougher, sites like Aweber want to make sure that you are not just some major spammer that is going to hurt them. While you can still use a free email address, it is recommended that you use one that is connected to your domain name.

Setup of a new email address is easy in cpanel and comes free with most hosting accounts. You may want to do that to avoid any issues in the future. Like Verena says above, you can then forward them to a free account if you want to.