Remember that I like almost all Sonic music. It's hard to choose my favourites. :(
(Sometimes it's fairly easy, sometimes it's hard, and sometimes it's really hard.)
These are mostly in order, with the best song generally being the first.
I included every Sonic game I could think of.
main series:
StH: probably Scrap Brain, then Spring Yard
StH2: Chemical Plant
SCD(English): probably Metallic Madness B or Collision Chaos
StH3: Icecap 1
S&K: Flying Battery 2
S3DB(Genesis): Panic Puppet 2, then Green Grove 2 (PP2 is a great level, and the music helps.)
S3DB(Saturn/PC): Volcano Valley... 2? (second music track, but possibly the first act)
SA: Emerald Coast 1, Open Your Heart, Final Egg 2, Icecap 3
SA2: Metal Harbor 1, then Pyramid Cave
Heroes: Metal Overlord, Bullet Station, Egg Fleet
portable:
StH for Game Gear: probably Labyrinth, then Scrap Brain
StH2GG: Underground (I can't remember all the music, though.)
Chaos: Mecha Green Hill
Triple Trouble: Sunset Park Boss, first level (forgot what it's called)
Blast: I easily remember which one I don't like... but maybe Green Hill is my favourite.
Drift: probably invincibility
Drift 2: probably Emerald Hill, though I can't remember
Spinball: I think it's Lava Powerhouse. It was used in the opening for a few seconds.
Tails' Skypatrol: I can't remember which one is my favourite. It might be the second half of the real second stage.
Tails Adventures: the first woods area (I barely got anywhere in this game.)
Labyrinth: Again, I don't really remember. Probably the first stage or something.
What's the 12th GG game? Is it so terrible that it has disappeared from my memory? :(
Advance: I've barely played this game. I think this was called Secret Base 2 or something.
(It's fast, and the background sounds NES-ish. ... I just checked, and it's #8 on the sound test.)
Battle: I think it's the beach place. Second might be the town area.
misc.:
Spinball: Lava Powerhouse
Mean Bean Machine: Password
Chaotix: Speed of Sound
Fighters/Championship: Giant Wing, then Death Egg's Eye
Sonic R: Reactive Factory
EDITS: I read RPG's post, and it reminded me that I forgot Panic Puppet's music!
According to my brother's track labels on his CD, yes, that SAdva one really is Secret Base 2.
(Listening to everything again, every music track in that game sounds NES!
That wasn't exactly the best way for me to describe it.)
Also, I think the Sonic Battle one is called Emerald Beach. (It's a battlefield.
The 2nd-place one is the map where that beach can be accessed.)