There are tons more out there that are fantastic, but here are my favorites. Also, I'm saving orchestral arrangements for their own video.
[0:18] - Chrono Trigger, Corridors of Time ("Chrono Resurrection" rearrangement by Mathew Valente) [http://www.opcoder.com/projects/chrono/media/]
[4:40] Kirby Super Star, Coliseum Battle ("The Saviour of Dreamland" by Sixto Sounds) [http://ocremix.org/remix/OCR02625/]
[9:47] Contra III: The Alien Wars, Ground Zero ("Dystopian Future" by dannyshock) [http://ocremix.org/remix/OCR02132/]
[12:32] EarthBound, In Winters There is a Snowman (Remix by Wolfen150) [https://soundcloud.com/wolfen150/snowman-2012-edit]
[15:32] F-Zero, Big Blue ("The Flood Plain" by JJT) [http://ocremix.org/remix/OCR01494/]
[20:44] Illusion of Gaia, Itory Village (Remix by Patrick Earls of the Purps) [http://www.youtube.com/watch?v=AeB5qIpYnmM]
[24:40] Street Fighter II, Guile Theme (A Cappella Remix by Smooth McGroove) [https://www.youtube.com/watch?v=4qwKCQ4M2Nw]
[27:00] Tetris Attack, Lunge Fish/Poochy ("Sound of the Dogfish" by halc) [http://ocremix.org/remix/OCR01780/]
[31:21] Mega Man X2, Intro Stage (Sega Genesis Remix by Weltall Id) [http://www.youtube.com/watch?v=Nmdy2W9ngZM]
[32:32] Stunt Race FX, Night Owl ("Thin Glow" by analoq) [http://ocremix.org/remix/OCR00909/]
[36:29] Star Fox, Corneria (Metal Remix by Ansgaros) [http://www.youtube.com/watch?v=1mqNA2WvsBA]
[39:14] Top Gear, Track 1 (Remix by mkronck) [http://www.youtube.com/watch?v=1lq0IGcSoZg]
[43:22] Gradius III, Accident Road (Remix by Sabao) [http://www.youtube.com/watch?v=nDTeelX8mRc]
[46:10] Legend of the Mystical Ninja, Lost Town Traveling ("Oedo Hop" by Palpable) [http://ocremix.org/remix/OCR01255/]
[48:50] Chrono Trigger, Millennial Fair (Remix by moonbowmusicmovie) [https://www.youtube.com/watch?v=bA0za1SUK4U]
[52:19] Breath of Fire, Battling/Sorrow ("His First Good Deed" by Trenthian) [http://ocremix.org/remix/OCR01093/]
[57:33] Mega Man X, Storm Eagle (Metal Remix by LennartAlsing) [https://www.youtube.com/watch?v=jKwyQXR7mQI]