I switched to Gmail several years ago for this reason. Every year or two I'd switch ISP's, or they'd merge with somebody else, and my e-mail address would change. I really like that Gmail has IMAP which makes staying sync'd between multiple devices a breeze. Google encourages you not to delete e-mails so I no longer have to worry about backing up my personal e-mail archive.
Hopefully if you cancel your account with AT&T they will forward e-mails to your new address for 6-12 months (although you may have to pay for that.)