So, there are two games I can recall that do this: L4D(2) and NoxiousNet Zombies mod for Gmod (not really a full game, but it has this). They both do an okay job, but it doesn't intensify my game experience as much as it could.
L4D's just feels like two soundbytes to tell you that either the hoardes are coming or someone's in danger, and the rest of the music just falls to the wayside.
The Gmod zombies dynamic music slides up and down quite well, but it tends to just be an audible meter for zombies in the area and does not always match game experience.
One suggestion is that, yes you can intensify music during teamfights, but definitely don't consider it as a simple "more action=more tempo" deal. It needs to be composed.
Most of the champions from each team are converging on one spot, game engine detects imminent team fight
A horn sound or bass drum hit at the first strike
Noxus/Demacia/whoever theme music
At each kill, it gets cheerier
At each death, a bit bleaker
As all die/ move on from the fight upbeat/bleary "teamfight conclusion music" plays
and please don't do this everytime there's a 1v1 or a small skirmish breaks out. SFX do well enough to provide excitement