How do I make a window move to the left half of my screen and another window move to the right half? On Windows 8, I type win + left and the current window becomes full-height and half the screen width and moves to the left. If I type win + right, the current window does the same except moves to the right.

This is so incredibly helpful. Is there a mechanism to do the same for Macs?
You can try Cinch and SizeUp apps to do that.

http://www.irradiatedsoftware.com/sizeup/

http://www.irradiatedsoftware.com/cinch/