When I played through the demo of Kingdoms of Amalur: Reckoning, I could never figure out how to rebind the movement keys. I prefer to use ESDF instead of the standard WASD, and while I was willing to adapt to WASD for the duration of the demo, I do not plan on purchasing the game unless I can use ESDF.
You can. From the menu, simply select Options > Controls > Controls and you're met with this screen:
You'll have to remap those keys first, followed by remapping the movement keys in the following order:
For some reason, mapping in another order bugs everything to F, rendering you immobile. If you follow this pattern, however, it works just fine!