Text (SC+errata): Counter target activated or triggered ability. (Mana abilities can't be targeted.) [Oracle 2006/10/01]
An activated ability has a "Cost: Effect" format. Look for the colon. A triggered ability starts with "when", "whenever", or "at". [Scourge FAQ 2003/05/30]
It can target delayed triggered abilities. For example, a card that says "Whenever a player cycles a card, you may remove target creature from the game. If you do, return that creature to play at end of turn." triggers when a player cycles a card and creates a delayed trigger that happens at end of turn. You can choose to target the "at end of turn" trigger when it is placed on the stack at end of turn. [Scourge FAQ 2003/05/30]
Game actions like the normal card, combat damage, or turning a face-down creature face up cannot be targeted. [Scourge FAQ 2003/05/30]