Is there a keyboard shortcut to move a window from one monitor to another?

UPDATE: Spectacle is no longer maintaned. The website forwards users to Rectangle, see Jack's answer or https://github.com/rxhanson/Rectangle/releases.

I just tried Spectacle, great app and it's free.

This is what it can do with the selected group of windows.

You need to activate accessibility support.

System Preferences > Accessibility > Enable access for assisted devices

As per comments: The accessibility option in Mavericks is now in

System Preferences > Security and Privacy > Privacy > Accessibility

There is yet another option that's completely free and requires no third-party app. Be aware that I've only tested this on MacOS latest version Catalina (as of now). For other OS versions see Create keyboard shortcuts for apps on Mac

1. Go to System Preferences
2. Select Keyboard and then the Shortcuts tab
3. Then on the list that appears select App Shortcuts
4. Add new shortcuts like this:
   • Click on the plus sign to add a new one, the Menu Title field has to match exactly the text that appears on the Window menu in every application: "Move to DISPLAY NAME" (To find the text just open the Window menu on any application)
   • Finally on the Keyboard Shortcut field enter the shortcut you'd like to use
   • Add as many shortcuts as you need to move any window between your displays!

I ended up using BetterTouchTool to do this. Overall I found it to be the most configurable. Here is a screenshot of my configuration, whereas Cmd+Ctrl+W moves a window to the next monitor.

If you have a 3 monitor setup (2 external monitors and the Mac monitor), you can set up the "Move Window to Next Monitor" to the right by doing the following:

1. set up a new shortcut, specify "Move Window to Next Monitor" as the Predefined Action
2. click Attach Additional Action and again specify "Move Window to Next Monitor" as the action
3. Voila, you can now move a window to the monitor on the right (a little hacky I know, but it works until the developer of BTT updates the app)

The only shortcoming of BetterTouchTool is poor Lion support (not all features are available) but it is available as an alpha release. This specific keyboard shortcut should work fine in Lion with the stable version, I reckon.

Moom can do this. It is not free, but Moom is a fantastic window management app. It lets you assign keyboard shortcuts to a variety of windows movements (including move to other display) and gives you an overlay of the OS X standard window controls.

Here are some screenshots:

Here is a list of window management apps from another AskDifferent post, What Window Management Options exist for OS X?. The only free option is Shiftit, and I'm not sure if it offers the functionality you are looking for.