If you can't get your mail to work on Snow Leopard after June 30, you might want to try one of these approaches
2. Delete your mail account from Mail preferences and set it up again using the Mail Server Information.
Some users have apparently encountered issues using this information in pre-Lion set ups (I haven't), Roger Wilmut has kindly provided instructions for those who find themselves with this problem.
I'm not sure what caused this problem with Mail. It was working one day, then not working the next. At least two people sent messages to my "mac.com" account and got automatic delivery failure messages -- and their e-mails were apparently lost forever.
When MobileMe "ended" I used my new laptop (running Lion) to set up my iCloud account and followed all the instructions to allow my MobileMe mail to keep working on the desktop (running Snow Leopard).
The "fix" that worked to get Mail working again was to simply delete my MobileMe email account and set it up all over again using my @mac.com address in the Preferences/Accounts window. (Winston's suggestion 2, above.)
Mail is now reloading about 9,500 messages, but everything seems to working as before.