Step 1: Elimination
The first statement is wrong because the direction follows Lenz's law. The second is wrong because the word 'always' is false, as eddy currents often cause losses.
Step 2: Material check
They also appear in magnetic materials such as iron cores, so the claim that they appear only in non-magnetic metals is false.
Step 3: Result
Induced currents flow in loops lying in a plane perpendicular to the field, which makes the third statement correct.
Final Answer:
The loops of eddy current lie perpendicular to the inducing field.
\[ \boxed{\text{(C) }\text{Eddy currents circulate in planes perpendicular to the magnetic field that induces them}} \]