Spectacle is a free and open source app that allows you to reshape, resize and reorder your windows with simple keystrokes. You set up your own keyboard shortcuts, and then use them to move windows around your screen. Split two windows on each side of your screen, top and bottom or left and right, or move a specific window to the foreground: Spectacle does a variety of different things, all with your windows. And it's free.
A Good User Experience, A Great Learning Curve
Spectacle starts you off with a few default shortcuts to do just a few of the things it's capable of, some of which were named above. In reality, it can do a lot: it can configure windows in just about any size and layout you'd like, work with any open window or with specific apps, and more. But getting it to do all of this takes some learning: it's expected that you'll eventually abandon the app's default shortcuts to make your own. The defaults are good examples to work off of and make it a little easier.
One of a Kind
There are apps that work similarly to Spectacle but none that, in our testing, are quite as flexible. If you're willing to spend some time learning how to use it, this is the best way to make use of your screen real estate, whether you have a lot or a little.