Window key+arrows hotkeys not working
Solution 1:
This can happen if you turn off what I think is called "Aero Snap" for the mouse. It also disables it when you use the Windows key.
To check if it's turned on or off go to:
Control Panel > Ease of Access Center > Make the Mouse Easier to Use
Look under the subsection "Make it easier to manage windows" and see if "Prevent windows from being automatically arranged when moved to the edge of the screen" is checked.
If it's checked, then that's likely the problem.
Solution 2:
I had a similar problem and determined the problem was that my windows key wasn't being recognized. I couldn't figure out why not though.. After about an hour of searching I realized the PC / Game switch on my logitech keyboard had slid to game mode... which causes win7 to disable the windows key.. even if you don't have the logitech drivers installed.
Solution 3:
The Dell Display Manager -- software pulished by EnTech Taiwan and so may show up by other names -- has an "Easy Arrange" feature which, if enabled, disables the normal Windows+Arrow key functions along with Aero Snap. If you see a yellow or red border around the screen or rectangular segments of the screen as you drag a window, this may be the culprit.
The fix for me was to disable this "Easy Arrange" feature of the software. The Aero Snap-related checkboxes in the mouse/keyboard ease-of-access settings mentioned in other answers had been turned on, but turning them off didn't restore the Win+Arrow behavior.