In classical times, deus ex machina was considered the equivalent of giving the audience the finger by some playwrights, insulting their intelligence by making everything better by introducing the so-called 'god in the machine'.
Tolkien did this once or twice in the hobbit, but that's almost excusable, being a children's book. Bombadil strikes me as a borderline DEM, being always there at the right time, and yet their meetings seem almost coincidental. Otherwise, most occurances can be fairly well explained in one way or another.
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