If a creature with a death trigger is exiled instead of going to the graveyard, does the trigger still happen?

A "dies" trigger is defined in the Comprehensive Rules as a triggered ability that uses the phrase "when [this creature] dies." Under CR 700.4, "dies" means "is put into a graveyard from the battlefield." If a creature is exiled instead — whether by a replacement effect like Rest in Peace or a spell's instruction — it never touches the graveyard, so the trigger condition is never met.

Replacement effects (CR 614.1) modify what happens to a permanent as it leaves the battlefield. When such an effect says "exile instead of going to the graveyard," the creature's destination changes before it ever arrives at the graveyard. Since the event "moved to the graveyard" never occurred, any trigger watching for that event simply never triggers (CR 603.2).

This is different from a creature that dies normally and is then moved from the graveyard to exile — in that case, the creature did pass through the graveyard, so a dies trigger would have already fired before the second move happens.

Concrete example: Your opponent controls Rest in Peace (which has a replacement effect exiling all cards that would go to any graveyard). You have a Solemn Simulacrum on the battlefield. When Solemn Simulacrum would die, Rest in Peace replaces that event, sending it to exile instead. Because it never entered the graveyard, Solemn Simulacrum's "when this creature dies, you may draw a card" trigger never fires.

In short: exile is not the graveyard. Any ability watching for a creature to "die" sees no triggering event when the creature is exiled directly from the battlefield.