While this is in no relation to the Chrome browser from Google, I'm actually contemplating moving over to a free e-mail service other than Gmail.
The biggest reason is lack of folder support. As a result of this, I have absolutely no way of filtering what e-mail gets forwarded onto my cell phone (and thus, receive alerts for). I do have some mailing lists and such I subscribe to, but I'd rather they just appear when I view the webmail page it's on.
Of course, the big thing I'd miss is Google's excellent spam filtering (I rarely see a spam message in my inbox).
Therefore, I'm wondering if people have experience with other webmail providers and could offer a suggestion.