Gosh, that's easy.

Chess.

PageRank.

Automated address reading in the postal system.

Protein folding.

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Just LLMs?

Very quickly finding texual needles in long-document haystacks. Can't generally do that with a plain text search unless you already know what the needle looks like, and doing it as a human is expensive — see Terry Pratchett's experience with German soup adverts.

Real-time translation within the price constraints of tourists.

Rapid prototyping.