Does a triggered ability that says 'whenever a creature dies' trigger when a token dies?

Tokens are treated as creatures while they exist on the battlefield. They have all the properties of creatures and can trigger any ability that watches for creature events, including death triggers. This is established by CR 111.1, which confirms tokens are permanent objects on the battlefield subject to the same rules as non-token permanents.

A creature 'dies' when it is put into a graveyard from the battlefield (CR 700.4). This applies equally to tokens and non-token creatures. The triggered ability checks this event and sees no distinction between a token creature and a card creature dying.

It is true that a token ceases to exist as a game object shortly after it reaches the graveyard (CR 111.7), but the death event still occurred and the trigger still fired. State-based actions and the trigger's existence are evaluated at the moment of death, before the token disappears. The trigger will go on the stack and resolve normally.

Example: You control a Goblin token and your opponent casts Doom Blade targeting it. You also have Cruel Celebrant on the battlefield, which reads 'Whenever a creature or planeswalker you control dies, each opponent loses 1 life…'. When the Goblin token dies, Cruel Celebrant's ability triggers, even though the token itself ceases to exist moments later.

So any 'whenever a creature dies' trigger — whether on your permanents or your opponent's — will see a token dying and will trigger accordingly, with no special exception for tokens.