When you say Shadowrun, this is what comes to my mind: http://www.youtube.com/watch?v=ome6XI_KuIw&list=PL2D5FC9FCF1AEF68C

A fave track from Castlevania 3 (Aquarius): http://www.youtube.com/watch?v=yyCXhfUqU88

My personal favorite from Mega Man 3: http://www.youtube.com/watch?v=iZ9ySQX_PF8

I'm ashamed, I haven't posted music from my #1 favorite game of all time: Zombies Ate My Neighbors!

Mars Needs Cheerleaders: http://www.youtube.com/watch?v=onPnJA4GG2w
Evening of the Undead: http://www.youtube.com/watch?v=JaqQQQJbAaA
Chainsaw Hedgemaze Mayhem: http://www.youtube.com/watch?v=3oF9NeU8MYc
Titanic Toddler: http://www.youtube.com/watch?v=JgCWp2nyWWA

And I forgot Blaster Master!

http://www.youtube.com/watch?v=7UknIyWcwAU

Dracula's theme in Super Castlevania 4:

http://www.youtube.com/watch?v=DM-4V12JLbk

I personally love this album. I wish to share it with you all. Some of you might have even heard of it before.

Preschtale by C-jeff

I'd say it's made by a genius.

More boss Boss Music:

Super Mario World Bowser Fight: http://www.youtube.com/watch?v=AMIzhWt_pvY

Sonic 2: http://www.youtube.com/watch?v=yzXwutv0yy8

Sonic 3 final boss: http://www.youtube.com/watch?v=RyoMQg3d5cs

And just because I like it...Sonic 3 Ice Cap Zone: http://www.youtube.com/watch?v=hYxlqTpZ-24

A thread about 8 and 16 bit music and nobody mentions any music by Chris Hülsbeck? Shame on you!

Here, have some Turrican II.

Turn up the volume and listen to the whole soundtrack. You are bound to find something you like because the soundtrack of this game is very varied. There aren't many soundtracks as good as this nowadays. :-(

I don't remember how many years I had 'The Great Bath' as my ringtone...

Contra: Hard Corps - Stage 1: http://www.youtube.com/watch?v=iYNLz8goZdE

Indeed not mentioning Chris in a 16bit music thread is a no-go. I also liked his songs played by a symphonic orchestra:
Turrican 2: http://www.youtube.com/watch?v=7dJrsmt9BOY
The Great Giana Sisters: http://www.youtube.com/watch?v=SSOS2uwqpfw

On the Amiga the 16bit music was huge, due to its advanced sound hardware. Artists using software like ProTracker and the demo scene brought out some very great stuff on the Amiga. Here is some more tunes from Amiga I especially enjoyed.
Chuck Rock: http://www.youtube.com/watch?v=8rm0eTagViU
Utopia: http://www.youtube.com/watch?v=0y6r0m3-ZAs
The Settlers: http://www.youtube.com/watch?v=r385tMuVwjg
Lotus 3: http://www.youtube.com/watch?v=L9-AqAdntVI
Cannon Fodder: http://www.youtube.com/watch?v=PiYuq6Ac3a0
Xenon 2: http://www.youtube.com/watch?v=1HnY56uq9uA

Xenon 2 and Cannon Fodder are classics. The Lotus Esprit Turbo Challenge series also had good music but I always preferred the title song of Lotus 2.

Also worth mentioning:

*) Shadow of the Beast
*) Deflector
*) Cybernoid 2

But when we start talking about Cybernoid it must be mentioned that the Amiga versions (while definitely good) are only a remake of the C64 versions by Jeroen Tel from the Maniacs of Noise. These are absolute genius:

*) Cybernoid
*) Cybernoid 2

But I'm going to stop now before I start listing more C64 music or I'm not going to stop for a few hours. ;-)

Everyone who is serious about 8-bit music has a permanent place on his hard disc for the High Voltage SID Collection anyway. Am I right or am I right? ;-)

Ninja Gaiden 1 (NES) - Act 2-2: http://www.youtube.com/watch?v=YCMg5-D799s

Darkwing Duck - Wolfduck Stage: http://www.youtube.com/watch?v=xcOD1w1rvng