This is the most recent "favorite Sonic music" thread I can find; forgive me if there's a newer one.
I need to start off mentioning Final Egg, "Act 2" in Sonic Adventure. This theme is so underrated. It really brings about a feeling that the player is on their last leg, about to be doomed if they don't hurry and act fast. Awesome guitar work, as usual with this soundtrack, but this one is just so amped up. Sadly, only Sonic gets to play the stage with this music, and it reverts back to the "Act 1" music later on. It would've been cooler to end with this one. But the first song is also a favorite of mine, just the second slightly above it in my book.
I'll also add Hot Shelter's "Act 2" music, used for Gamma's stage and the second half of Amy's. It's similar in a way, but more electronic and not as "impending doom" vibe.
Honestly Sonic Adventure is just full of amazing stage themes, and they add so much ambience and atmosphere to the game. Some of my favorite standouts, besides the ones already mentioned:
Speed Highway, "At Dawn". Didn't think a piano ballad type song could work for a stage like this, but it does.
Ice Cap, the snowboarding music. How can you not get pumped up hearing this??
Casinopolis, "Dilapidated Way". Just has a very "cool" vibe to it.
But really I could easily listen to any stage theme from this game and enjoy it.
For Sonic Adventure 2, my favorites are: the Knuckles rap songs (of course), Eternal Engine, Security Hall, and Cosmic Wall. Oh and not a stage, but the Chao Karate music from SA2B is godly.
Sonic Heroes was meh to me but I enjoyed some of the music. Ocean Palace, Power Plant, Hang Castle, and Frog Forest mostly.
Oh and Sonic Shuffle... the end credits theme was too good for this game.
Moving onto Classic 16-bit games...
For Sonic 2, my definite fav is Casino Night, 2-player. Rumor has it, it was meant for Cyber* City Zone, a scrapped level. (*Yes, Cyber. Not Genocide. That was an error. It wasn't meant to be called that. Stop calling it that.) But it fits the casino very nicely, similar to Dilapidated Way from SA1. But the entire game's soundtrack is amazing.
For Sonic 1, my favorite is Scrap Brain, followed by Marble, then Spring Yard. Can't get enough of these songs.
Sonic 3... hard to pick favorites. Again, could just say "the entire thing". But I'll point out Death Egg Zone because this one often gets overshadowed by the other great music.
Also I'll thrown in the Mega Drive/Genesis version of 3D Blast, because it had some great music in Rusty Ruin Zone and Diamond Dust Zone (curse Chronicles for ruining this one).
8-bit games also had some great songs!...
Sonic 1: Bridge Zone (which Janet Jackson later copied?), and my favorite, Scrap Brain Zone. I love this one more than the 16-bit one tbh. Really sinister sound to it.
Sonic Triple Trouble: the level when you're on a train. Lol. Forget the name but this song is great.
Sonic Chaos: Mecha Green Hill Zone, this is my jam.
Sonic 2: Crystal Egg Zone. Even though I never got that far. ;-;
Now for the Advance games...
Advance 1: Ice Paradise Act 2, which is very happy and upbeat. Angel Island Zone. And my favorite is Egg Rocket Zone. Why do final levels always have such awesome music?
Advance 2: Sky Canyon. Level was hell, but the great music helped me tolerate it. Music Plant had fun music to go with its theme as well.
Advance 3: Route 99 had a nice theme, too bad the level was pretty awful. Twinkle Snow zone had good music too.
Also, for Advance 2 & 3, the 2-player music (with only 1 GBA cart) was amazing. Should've been in the main game! And in all of them, the Chao Garden mini-games had a fun theme.
And of course, can't forget Sonic Battle. Probably enjoyed this one more than the Advance trilogy tbh. Tails, Knuckles, Amy, Cream, and Chaos all had great music for their arenas, and the end credits theme was... too emotional. ;-;
I think that's all I can think of for now.