Just to get it off the list, I'll put the Adventure series on here. It's quite easier because each character has their own genre which was chosen to fit their personalities, especially in the second game, though as time goes on and musical associations change, perhaps their genres may shift.
Sonic: You guys have probably exhausted this enough, but you're quite accurate. His themes are very guitar-oriented, ranging from rock, to punk (or ska-punk, as was mentioned before), to even some metal influences in the riffs (ever noticed how the intro for "City Escape" vaguely resembles the intro for "2 Minutes to Midnight" by Iron Maiden?). Basically, anything that seemed "urban" and was associated with "cool" stuff at the time, not unlike a Tony Hawk soundtrack. What I wonder is how his musical tastes would evolve as our own tastes have over time. Perhaps a little more dubstep/house influence since they've outgrown rock these days?
Tails: Keeping up with his personality as a "follower of Sonic but with his own twist", his own musical genre is a similar mix of rock, but much more upbeat and idealistic, with a few electronic instrumentals thrown in there for good measure, because we all depend on Tails when our inventions are broken.
Knuckles: All of his music has a lot of African-American influences, consisting of old-school hip-hop with jazz thrown in the mix. It might reflect his "black" roots, what with the dreadlocks and colors (I heard rumors he was supposed to have a Jamaican accent once but they scrapped it? Now that would've been interesting...) Lyrically, they fit Knuckles' personality quite well, bragging about how tough and unafraid he is, or claims to be.
Amy: Hm... her genre doesn't seem quite so solidly grounded as the other characters are, possibly because she was only playable in SA1, which didn't have the solid genre-per-character themes like the second game. Her theme "My Sweet Passion" definitely, and obviously, has a strong bubblegum influence, but has some interesting twists in there as well, with some hints of sax. Other themes associated with her go anywhere from rock-influenced to... eh, what's the genre name here... anyways, whatever genre it is, but all very, very upbeat.
Eggman: He's mad. He's bad. And he's a science man. His music is full of electronic instrumentals and techno influences, but there's actually a lot of rock influences as well. His style could be summarized as electronic rock. I would like to see more epic instrumental music like he had in '06, but, heh-heh... maybe that reflects his status as a secondary villain who doesn't deserve the epic instrumental music... hehehehehehe....
Shadow: When he was introduced, he was a very mysterious, dark, angry, and even angsty, with a technological background (created on the ARK by a scientist, and also wears some sweet jet shoes). Therefore, his music genre was Industrial/Techno/House, all completely electronic. The distorted vocals are reminiscent of NiN, which fits the Angry/Angsty dynamic. After his own game, he gets a much more rock/metal influence though, because at that point he became less of a mysterious enigma and more of an "action anti-hero" type guy.
Rouge: Being the lovely seductress she is, she lives up to her fancy French name with some fancy music. They feature tons of sax and female vocals; sensual music like jazz and blues, but with a much higher tempo and more upbeat to fit the action-packed nature of the game.
Then again, I'm not the most genre-literate person out there, so I might be off in a couple genres and there might still be room to shoehorn a couple more genres here. You go ahead and tell us that.
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