If a land is animated into a creature and then destroyed, does it go to the graveyard as a creature or a land?

When a permanent leaves the battlefield, the game uses its last known information — the characteristics it had at the moment it left — to determine what it is for any relevant purposes (CR 112.7a, 400.7). If a land was animated into a creature when it was destroyed, it was both a land and a creature at that moment, so it arrives in the graveyard as an artifact, enchantment, or whatever it was, plus a creature and a land.

Practically speaking, the card in the graveyard itself reverts to its printed characteristics once it leaves the battlefield, because continuous effects (like animation spells) do not follow permanents to other zones unless specifically stated (CR 400.7). So the card sits in the graveyard looking like a normal land card again — but any replacement or triggered effects that cared about 'a creature dying' or 'a land being put into a graveyard' will both have triggered correctly, because at the moment of death it was both.

This matters for effects like the landfall-in-reverse question, or for cards that trigger when a creature dies versus when a land goes to the graveyard. Both types of triggers would see the permanent and trigger appropriately.

Concrete example: You control a Mountain that has been animated by Awaken (making it a 4/4 land creature). Your opponent casts Murder, destroying it. The Mountain goes to the graveyard. Any effect that triggers when 'a creature dies' (e.g., Blood Artist) triggers, AND any effect that checks if a land went to the graveyard also applies — because at the last moment on the battlefield, it was both. The card in the graveyard, however, is just a plain Mountain card.

Key rules: CR 400.7 (objects changing zones retain last-known info for triggered/replacement effects), CR 112.7a (continuous effects end when the permanent leaves), and CR 700.4 (the 'dies' terminology applies to creatures specifically, confirmed by the last-known creature status).