Why is this happening in my UV Unwrapping? I just modeled my first character, and have performed my first UV wrapping. Everything looks ok, but the UV's for the Eyeballs seem to fill the background behind the other figure elements, and are stacked on top of each other. I've tried scaling them down, but there seems to be layer after layer after layer. Pardon the pun but is this normal?
You do not have seams on the eye spheres, so either add seams, or try unwrapping with Smart UV Project or Sphere Projection.

What you are seeing is Blender unwrapping every individual face on top of each other.

I would highly recommend that you read the Blender manual section on unwrapping before continuing.

Also, see this question if you want details on unwrapping spheres in particular: 

What is the best way to unwrap a sphere?