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Beavers only appear in the Game Boy Advance version, Dawn of Souls, and all subsequent releases. They are located in one of the sub-basements of the bonus dungeon Whisperwind Cove, where a side mission involves a dwarf asking Warriors of Light to help him retrieve his lost giant beavers by speaking to them and placing them in different rooms.
The Beavers make their first series appearance in the original NES version as a race that lives deep within the Snow Cave. Guy is able to speak to them, and asks one of them about the Goddess's Bell, which he is told is in a nearby room guarded by a vicious Adamantoise.
Beavers make an appearance in Final Fantasy XIV: Shadowbringers. They are enemies to the Pixies of Il Mheg and possess an ability to turn pixies into more beavers.