When you compose a new email message, Mail will frequently save drafts of the message in the "Drafts" folder. Messages will also stay here if you save them to work on later. Some people have found that these draft email messages will persist in the Drafts mailbox despite them having completed and sent the message.
This seems to happen with IMAP accounts, and generally is because the draft message is being synchronized with the server's Draft mailbox. This problem may be more prevalent with Gmail accounts which have special or slightly altered implementations of the IMAP protocols that can lead to some odd behaviors or incompatibilities with some email clients.
Storing draft email messages on the server is only necessary if you use more than one computer to compose the same emails. In many cases people have this feature enabled when they rarely use it, so if you do not need it and are experiencing draft email buildup, try disabling the feature. To do this, go to the Account preferences and uncheck the option in the "Mailbox Behaviors" tab.
If you do need the drafts option, you can try removing Mail's preferences and recreating your email accounts, which should hopefully clear any odd behaviors with how Mail is connecting to the server. The preferences file is called "com.apple.Mail.plist" and is stored in the /username/Library/Preferences/ folder. Keep in mind that doing this will require you to set up all of your email accounts again, which may be impractical for people with many accounts. Keep a copy of your old preferences file so you can quickly restore your old settings in necessary.