There are several alternate costumes that you can unlock in Injustice: Gods Among us on the PS3, WiiU, and Xbox 360.
Some of them require access to the Injustice: Gods Among Us game on an iOS device (iPhone, iPad, etc.) so I've listed those separately.
This is currently a running list, so I'll be adding more as they're found. Please leave comments if you have found some that aren't on this list.
Here are the alternate costumes you can unlock, and how to unlock them.
Boss Grundy – Complete Classic Battle Mode with any character
Godfall Superman – Complete Story Mode with any character
Lex Luthor Alternate – Complete S.T.A.R. Labs with at least one star
New 52 Flash – Create a WB ID, or login to your WB account if you already have one
Yellow Lantern Alternate – Win a ranked online match