In The Elder Scrolls V: Skyrim for the PC, PS3, and Xbox 360, you can drag bodies around the same way you move other objects around in the world.
If you’re having trouble figuring out how, that’s because there really isn’t a prompt for it, it just says “Press such and such button to loot”, but if you press and HOLD the button you normally press to loot the body, you will grab the body and drag it with you as you move.
The best way to move a body isn’t by dragging, but by grabbing the head or ankles and picking it up off of the ground completely to move it. When trying to drag a body, the ground creates a lot of friction, so you’ll usually end up letting go of the body multiple times before you’re done.
Moving other objects around is the same, simply press and hold the button you would normally press to TAKE the object to pick it up and move it. This is not considered stealing either.