I think the most famous mainstream example, besides Sonic CD for a certain generation, is probably Gran Turismo. Quoting The Cutting Room Floor's extensive article:
The original, Japanese release of Gran Turismo paid direct homage to the influence of T-Square on the soundtrack of sports mechanics shows broadcast on Japanese television in the Eighties and Nineties.
Instead, the Western branches of PlayStation thought their own broad audience would miss on the musical reference and appreciate mainstream artists which also happened to be signed on a Sony Music label. Timing-wise and sales-wise, Gran Turismo is pretty much the coronation of PlayStation’s victory over its competitors, with a first party Sony Computer Entertainement game redefining an entire genre, selling absolute gangbusters and leaving a genuine cultural impact on Western society. So I can’t really blame Sony here for trying stuff. They probably did something right with regards to most of the game’s audience, and I don’t think it’s a bad soundtrack. So it should qualify for this thread. I do feel sorry that so many people missed on the amazing Japanese soundtrack.
This mainstream success culminated with an actual popular band, The Cardigans, naming their new album Gran Turismo because they were fans of the game, and that album’s hit single My Favorite Game (get it?) replacing Moon Over The Castle in the Western intro movie of Gran Turismo 2.
Here is the Japanese intro, with a brand new version of the famous track.
Here is the North-American intro, with the Cardigans’ hit song.
Here is the European intro, with the Cardigans’ hit song, but remixed by Faithless.
From that point on, it became pretty standard for each region to get their own variation of the soundtrack for each new episode. I believe things finally went global in the PS3 era, which also coincided with the decline of Gran Turismo as a brand, and the decline of racing games overall in the video games landscape.