EDIT: Seems dynamic music is back in style in some very recent games, many of which I haven't really played yet. Good. 
For me, it's dynamic music, the kind that some games had that adjusted moment by moment to what was happening in the game.
The best-known example of this in the 90s game TIE Fighter, where the moment more enemy (or allied) ships showed up the music would have a little additional flourish to acknowledge the shift in battle. There were pre-battle tension tracks, battle music, complications of battle, grandiose flourishes for the arrival of enemy or even allied capital ships, and victory and failure music all ready to flow into the next seconds of the game.
A lesser-known but still excellent example of this was in Ultima Underworld and its sequel, where drawing a weapon had its own special "preparing for battle" tension music, getting attacked had a jump-out-of-your-skin joltingly sudden musical start that actually scared me as a kid when I got ambushed, music for battles going well, going poorly, victory and defeat.
I wish more games did those sort of second by second musical changes, but they've sort of fallen out of fashion for the most part. 
I feel like cel shading never took off they way it could have. Outside of anime style games it seems like it always takes a back seat to realism which sucks because it's looks rad as hell. XIII and Viewtiful Joe are two examples that stick out in my memory, plus Wind Waker pissed off so many Zelda fans who wanted a grimdark Peter Jackson LoZ game. It was great.
It's really difficult to make it not look bad in many cases, it often comes out blotchy
Hi-Fi Rush if a recent non-anime game that is cel shaded but it still has a tinge of anime vibes.
I never actually owned Viewtiful Joe, but I did have the demo disc and I played through it like a million times. Loved the shit out of that demo.
BOMB RUSH CYBERFUNK
I must say BRC is the finest game ever made and it slaps