Illustrator - yes in the align palette check align to artboard
Photoshop - No offical command, but YES you can do this! Select atleast one floating layer and your background layer. Click on the align icons up in the options bar. Will align to your background layer.
This is really the only usefulness I have found for a background layer to exist in photoshop. Out of curiosity, does anyone else have any other usage for Photoshop to have a background layer???
-align if all elements are on different layers.
If I had to guess, I'd say that the background layer was created to be sort of a stage to help "ground" people in the design process. I'm sure you know this Mike, but everyone does not...You can rename that backround layer and then you can move it like the others.