Repositioning and resizing windows isn’t probably the most entertaining subject out there, but as we do those two all day long, let's talk about it once and for all.
I remember having blogged about this subject on another blog about 3 years ago, and today, I'm finding myself talking about this very same subject to various mac users (since it's a native feature on windows), having failed to deal with the issue.
CMD + ALT + LEFT/RIGHT
Cut a long story short. The app is called Spectacle. It’s very cool, simple, non-obtrusive and free. And I've been using it for ever now.
Once installed, you’ll have to enable access for assistive devices.
Review your shortcuts, change them if you wish, and start getting more productive with your open windows...
You can run the app in the background but I suggest you add it in the status menu.