Can you counter a triggered ability with Stifle?

Stifle reads: "Counter target activated or triggered ability." Triggered abilities are indeed legal targets for Stifle. When a triggered ability triggers, it is placed on the stack as an object (CR 603.3), and at that point it can be targeted and countered just like a spell — it simply uses the word "counter" rather than requiring a spell to target it.

Under CR 609.3, if a triggered or activated ability is countered, it is removed from the stack and its effects never happen. This is true even for abilities that say "this ability can't be countered" only if they specifically have that text — otherwise Stifle works normally.

It's important to remember that Stifle does NOT counter spells, only activated or triggered abilities. So it cannot counter an enters-the-battlefield spell itself, but it CAN counter the triggered ability that fires when a permanent enters the battlefield (e.g., the "enters with counters" or "draw a card" trigger).

Concrete example: Your opponent casts Mulldrifter and it resolves, entering the battlefield and triggering its "When Mulldrifter enters the battlefield, draw two cards" ability. In response to that trigger on the stack, you cast Stifle targeting that triggered ability. The trigger is countered (CR 609.3), and your opponent draws no cards.

Stifle is also commonly used against fetch land abilities (activated, not triggered), but for triggered abilities — like Snapcaster Mage's ETB, Rampaging Ferocidon's life-loss trigger, or Rhystic Study's draw trigger — Stifle is fully legal and effective.