Apple - Mail.app - keyboard shortcuts to move mail and jump to folder

To do this, you need to display the Favorites Bar, which you can enable by going to Mail » View » Show Favorites Bar.

You can add any folder to this bar, which you can then easily switch to with Command1, Command2, etc.

CtrlCommand1 moves the currently selected email(s) to the respective folder.

Here is a shortcut that you can use easily as described by Philip Mat, No needs of any app, it is built in Mail using the help shortcut.

http://philipm.at/2011/mail_quickly_file.html

1. Press Cmd-? or Cmd-Shift-/ to access the Help > Search menu.
2. Type in the name of your folder.
3. Press arrow down once for Move To or twice for Copy To and hit return.

MailActOn is an extension that provides fast filing of email messages in Mail.app. It is a paid extension though, but I find the $24.95 price tag reasonable for the productivity gains.