Music by Sega...

[Kid Dynamite]

Sega arcade titles definitely had some awesome music from around '85 starting with Space Harrier up until the early 90's. Not only was the music awesome, but Sega was on the forefront of arcade gaming technology for a long time. In Japan their reign continued even longer. I definitely love me some Sega arcade music, I'm partial to Space Harrier personally. Here are some console picks to go with the already selected arcade tracks:

Revenge of Shinobi: http://www.youtube.com/watch?v=Wv-J3eKTAm4&fmt=18
Sonic the Hedgehog 2: http://www.youtube.com/watch?v=H9283TWaAq0

Now that the Sega love has been thoroughly documented, I think composers of some other companies deserve some recognition for their work. I agree with an earlier post that Nintendo had some great themes with Metroid probably being my favorite soundtrack, but the most consistent killer soundtracks in my opinion came from composers for Capcom and Konami. I have to give the nod to Konami generally speaking as their games continued to keep outstanding soundtracks beyond the NES years:

Ducktails: http://www.youtube.com/watch?v=KF32DRg9opA
Mega Man 2 (This and Castlevania 3 had the greatest soundtracks on NES for my money): http://www.youtube.com/watch?v=5G8XQ89risA
Castlevania 3: http://www.youtube.com/watch?v=qTVn0mwc66Y
Castlevania Bloodlines: http://www.youtube.com/watch?v=dSn1f-Xz8go
Contra 3: http://www.youtube.com/watch?v=xM4iZvrCb2w
Sparkster: http://www.youtube.com/watch?v=RZ3ZVBM4g6w

Back to arcades, gotta agree with the Atari love, here's one of my favorites of all time:
Paperboy: http://www.youtube.com/watch?v=5byxOWx9SV8

The late 80's early 90's saw some great music from Konami composer Michiru Yamane among others:
Detana Twinbee: http://www.youtube.com/watch?v=r3_V_hnYj84&feature=results_video&playnext=1&list=PL121AA16EC61EFA9B
X-Men: http://www.youtube.com/watch?v=NVr0S2dixJg

....and Capcom arcades of course had memorable themes:
SFII: http://www.youtube.com/watch?v=ot7AW_z5Tes
Strider: http://www.youtube.com/watch?v=OZaPaO_iEYw

.....but it's finally time to give arcade shmups some love on this thread:

Air Gallet: http://www.youtube.com/watch?v=Cgb2xUAqLAM
Great Mahou Daisakusen: http://www.youtube.com/watch?v=C-NlHMQTwnk
Hotdog Storm: http://www.youtube.com/watch?v=4H_mVM1X1tU

....then there's the master, Namiki:
Battle Garegga: http://www.youtube.com/watch?v=Szr0TSXcWok&feature=related
DoDonpachi Dai-Ou-Jou: http://www.youtube.com/watch?v=TS_9LXL0K_k
Ketsui: http://www.youtube.com/watch?v=C20DBHIx1oU
Deathsmiles (kinda a cheat for arcade list since it uses recorded instrument samples): http://www.youtube.com/watch?v=6M7dYQorsGI