Sometimes Mail seems to be stuck (especially when you are trying to quit it). Many times, people force-quit Mail because they think it’s frozen, when actually Mail is busy synchronizing folders, or getting mail, or otherwise doing what it’s supposed to be doing. (If Mail is busy, let it finish. Force-quitting could cause damage to the Mail database.)
You’ll learn a lot about Mail by showing the Activity window (in Mail, go to the Window menu, then to Activity), and you’ll learn even more by looking at the Connection Doctor (Window menu, Connection Doctor).
Leave the Activity window open in a corner of your screen and keep an eye on it as you use the Mail program. I think you’ll find that Mail is quite the busy bee, and when you can see the program working you’ll be much less likely to give up on it and force-quit. I don’t leave Activity up all the time, but when things seem slow I look to Activity to see what’s going on.
As for the Connection Doctor: it’s needed less often, but when you’re not getting mail or not able to send mail it is interesting to see whether your Mac’s Mail app is successfully logging into the email servers or not.