Material 'Offset'

The ‘Size’ values affect my texture, but the ‘Offset’ doesn’t seem to have any affect. Is there a way to scroll (animate) textures on an object?

If you use Clip option then Offset does work imo. Texture could be movie for blender internal render. Cycles does not support this yet.
You can animate any numeric parameter for textures. Place mouse cursor over numeric field, insert keyframe, change to next frame, change parameter and insert another keyframe. Alt-a animate or render animation to see internal procedural texture changes. It’s possible to assign several image textures for object and animate influence for them.