Two songs? Just two?! I make my own rules and pick some of my random favorites.
Sonic the Hedgehog:
Labrynth Zone - I love the somewhat laid back, but very positive feel of this, it fits Sonic really well in a strange way. Sonic music is never going to be like this again, sadly.
Sonic the Hedgehog 3:
Final Boss - I love this one, makes you feel like this is your last chance, and the world's only hope. Pretty damn epic.
Sonic Adventure:
Welcome to Station Square - I think this is the most under appreciated Sonic song of all time.
Sonic Adventure 2:
Rumbling Highway - I personally think this is the best song ever for Tails, it should have been his theme song. This is my favorite song from Sonic Adventure 2, it is in my opinion the perfect mix of new and old age Sonic style.
Sonic Unleashed:
Shamar Adventure Field at Night - Absolutely brilliant song. Very high quality and long.
Sonic Spinball:
Lava Powerhouse Zone - Brilliant track. I love how dark it is, but is not obnoxious like most of the later dark Sonic stuff.
Sonic 06:
Tropical Jungle Swamp - It pisses me off how wonderful this song is. Especially later in the song, around 2:20, which was actually cut out of the game (probably because it sounds too much like older Sonic games)
Anyways, this last one was done by Takenobu Mitsuyoshi. If you listen to it closely you can actually hear his voice in the back a bit. I love it!