Hi. Try force quit to close the mail application (click the Apple icon and then Force Quit). You should see a window with the list of apps running. Just click the mail app and quit. Backup your mail then delete the preferece list - com.apple.mail.plist. You can find this in ~/Library/Preferences.
If the solution that AES gave you doesn't work...
Open Activity Monitor (applications > utilities).
From there you can find all the processes that are running and just find mail and quit/force quit it. Just don't quit other processes.
I’ve seen the exact same thing for some time. The odd thing is Mail.app isn’t frozen and doesn’t say ‘Application not responding’ in the Force Quit Application window like you would expect it to. But ‘Quit Mail’ and several other menus are greyed-out. It is like part of Mail.app quits then halts the quit process leaving it in a semi-quit state. But the app is still open and you can access the menus.
This bug has been around for a while. NOT fixed in 10.6.8.
I wonder if anyone is still experiencing this in 10.7.x?