If you mean Hydra-based Web APIs that closely resemble current JSON-based APIs, than I guess the answer is that no "significant site or project" has published anything production ready yet. Quite of a few people and a handful of startups mentioned that they are working on it. If, on the other hand, you include Triple Pattern Fragment servers, which are based on the Hydra Core vocabulary, then there are actually quite a few significant projects that serve their data using Hydra. There's even a post claiming there are more than 600,000 of them :-) You can also find a short list of prominent projects on http://linkeddatafragments.org/data/.
Disclaimer: I'm the chair of the Hydra W3C Community Group and one of the core designers of JSON-LD.