I mentioned it in a previous post but Harry Mason from Silent Hill on the PS1 would react to how much you make him run.
He breathing becomes shallow and more rapid the longer you make him run. He also physically moves his shoulders and head as he pants and if you don't allow him to take a break he just stops running until he catches his breath. So I suppose we can say Harry too, has a heartbeat.
I also recall another game having heavy breathing mechanics to indicate when enemies are closer, it might have been Penumbra on Steam. I guess that character too, has a heartbeat.
Those would be actions and tension affecting the breathing patterns of NPC's and main protagonist
Edit: Isaac from Dead Space too. I recall hearing rapid panting after fighting.
I would not watch the whole video (go to 04:10) but towards the end Isaac fights two enemies while in space and you can hear his breathing become more pronounced. You can even hear his heartbeat speed up as he gets hit.
That's an amazing detail. Because you're in space, the only sounds you can hear are what's going on in the players suit and the sound design was sure to make it interesting.
If I recall correctly it would get louder the closer you're to death which alerts the gamer to use a medkit if they couldn't see the spinal health indicator.