EDIT: Just want to say that these are better than I expected. As good or better than about half the ambient music recommendations I get on Spotify.
• Disasterpeace's most famous soundtracks all incorporated some measure of procedural music happening at runtime — Fez, Hyper Light Drifter, The Floor Is Jelly, Mini Metro... this ranged from simple mixtures of tones and textures at random intervals to very advanced, tightly integrated (re-) composition systems.
• Most games will dynamically mix different "stems" together based on the action in the game. Amon Tobin's soundtrack to Splinter Cell: Chaos Theory is a great example of this, but it happens in pretty much every AAA game now (and most indies, if not something more ambitious like the above). Another great example was Banjo-Kazooie on the N64. In simpler cases there are 3 or 4 different variations of each piece of music, but it's not uncommon to find a game with many more. Couple that with Fmod to apply filters at runtime (like a lowpass when diving underwater) and you have a very lively, dynamic soundtrack that adapts to the gameplay.
I could list a ton more examples, but that'd be tiring. A key point is that while this music is procedural, it's not generative. In other words, while it's common to find games where existing music is remixed dynamically, you rarely find games where the music is being composed on the fly.
Another interesting aspect to consider is the relative rarity of generative or procedural sound effects. Most sound effects are played back as-recorded, with perhaps some Fmod filtering. Mario Odyssey one-upped this by playing different sound effects depending on the moment-to-moment chord changes in the music, so that the sound effects would harmonize and "play along" with the music — to beautiful effect. But rare is the game that fully dynamically generates sound effects at runtime.
A more generative example is the music in Portal 2. There are several aspects to its music that are subtle, purely generative and integrated with the gameplay. For example, the each receiver for the laser beams start playing an additional, random voice over the background music track as long as it is hit by a ray. It is a bit faint, bit it is there. It becomes cool in those levels where you have several of them next to each other They are starting to play a randomized concert while you are solving the puzzle. Someome made a long and elaborate writeup about this and other aspects of the game's music, but I can find it now.
It is a but funny because games shifted away from using sound synthesis amd sampling for music to studio recorded tracks over time as they started to have enough storage space for it. But this now limits how you can process the music to make it dynamic.
Edit: here's the talk: https://www.youtube.com/watch?v=zKJ_XuQjjiw