I recently ran into a problem where all the e-mails I tried to send in Mail got stuck in my outbox and were not sent. After reading posts on the Apple Support Communities website and doing some troubleshooting of my own within Mail, I reached a solution to the problem. When I first realized I could not send e-mail using a certain e-mail account of mine, since all e-mails were getting stuck in the outbox folder, I checked my available servers. I did this by opening the preferences window, clicking on the accounts tab, then clicking on the outgoing server pull-down menu. In the pull-down, I saw that the server I wanted to use was listed as "offline." To fix this problem and get the server back online so that I could send e-mail (as I could with my other account that was not listed as "offline"), I selected the outgoing server pull-down once again. In the menu, I selected "edit server list." On the page that pops up afterward, I highlighted the server I wanted to use. This way, I could see the information associated with the server. With this information in front of me, I realized that for some reason there was no password entered in the password field even though the "Authentication" setting was set to password. I entered my password associated with the e-mail account I was having problems with and "walla." The server was back online. I could send e-mails again without them getting stuck in the outbox!
This problem popped out all of a sudden for me and got me quite frustrated. I hope that this brief walk-through helps out some people out there having a similar issue. Best of luck!