This has possibly changed with the more recent Unity updates. My animations look fine and move the root position of the character in preview mode. However, in the game the character does the animation without moving position, and it looks really bad.
The player seems to have this awkwardness with or without a rigidbody. He seems to be moving just fine with walk and run animations. Are there any known issues with using mecanim to perform animations that cause the character to move around a bit?