Can you counter a triggered ability with a spell that says 'counter target spell'?

Spells and triggered abilities are two distinct types of objects that can exist on the stack. A spell is a card (or copy of a card) that has been cast, while a triggered ability is an ability that triggers from a condition being met and is placed on the stack separately from its source card. Because they are different object types, effects that target one do not affect the other (CR 113.1, CR 112.1).

When a card says 'counter target spell,' it can only target objects that are classified as spells on the stack — instants, sorceries, enchantments, artifacts, creatures, planeswalkers, or battles that have been cast but not yet resolved. Triggered abilities (and activated abilities) are explicitly not spells (CR 112.1a), so 'counter target spell' cannot legally target them.

To counter a triggered ability, you need an effect that specifically says it counters an 'activated or triggered ability,' such as Stifle or Disallow. These cards reference abilities on the stack as a distinct target category (CR 114.4).

Concrete example: Your opponent's 'Enters the battlefield' trigger from Gray Merchant of Asphodel is on the stack. You cannot cast Counterspell to stop it, because the trigger is not a spell. However, you could cast Stifle, which reads 'Counter target activated or triggered ability,' to prevent it from resolving.

The key rule is CR 113.5: triggered abilities on the stack are not spells and are unaffected by anything that only references spells as targets.