Can you choose not to put a triggered ability on the stack when it triggers?

When a triggered ability's condition is met, it triggers and is placed on the stack automatically at the next available opportunity (usually the next time a player would receive priority). The controller of the ability does not get to choose whether the ability goes on the stack — this is mandatory under CR 603.3.

The only exception is when the triggered ability itself contains the word 'may.' In that case, when the ability resolves (not when it triggers), the controller chooses whether to take the action. The ability still goes on the stack regardless; you just opt out at resolution (CR 603.3b).

Some older cards used 'may' in the trigger condition itself (e.g., 'Whenever X, you may have this trigger'). In those rare cases, you can choose not to put the ability on the stack at all. But this is because the card explicitly says so — not a general rule.

Concrete example: You control a Bronze Bombshell that was given to an opponent. When it triggers dealing 7 damage to that player, you cannot simply choose to skip it — the triggered ability is placed on the stack automatically and will resolve unless countered.

In summary: triggered abilities are automatic. You cannot choose to 'skip' placing a triggered ability on the stack unless the card text explicitly grants you that option (CR 603.3, 603.3b).