If a spell is countered and a copy of it was made, does the copy also get countered?

When a spell is copied, the copy is a completely separate object on the stack. It exists independently of the original, so any effect that targets or affects the original spell does not automatically affect the copy (CR 706.10).

Counter spells and abilities typically target or refer to a specific spell object. Unless the countering effect says something like 'counter target spell and all copies of it,' it only counters the one spell it was aimed at. The copy remains on the stack and will resolve normally (CR 114.1, 701.5).

There is an important distinction, however: if the reason a spell is countered is that all its targets became illegal, and the copy has the same targets that also all became illegal, then the copy would also be countered by the rules — but for its own independent reason, not because the original was countered (CR 608.2b).

Concrete example: Your opponent casts Lightning Bolt targeting your creature. You cast Reverberate to copy it. Your opponent then plays Counterspell on the original Lightning Bolt. The copy of Lightning Bolt is still on the stack and resolves normally, dealing 3 damage to your creature.

So the bottom line: copies live and die on their own merits. Countering the original leaves any pre-existing copies completely unaffected unless a specific card effect states otherwise.