http://www.surfing.net/ultima/bard/u6midi/Stones.midThis one's rather sad, especially taken into context. We will probably never see RPGs as good as the old Ultima games, ever again.
http://www.midishrine.com/dritidet/mpc/Doom/level2.midThis is the music to the second level of Doom. For some reason, it reminds me of porno music. Unfortunately, I haven't convinced a girl to "experience" this music with me. For one thing, it's too short.
http://www.midishrine.com/dritidet/sns/Chrono_Trigger/w1000a.midChrono Trigger. Another kick ass game that they don't make anymore.
http://www.hamienet.com/16517_The-Unforgiven.midThe Unforgiven. The original song is overproduced pop music and a sellout for Metallica, but damn, the MIDI smokes. There's just something about MIDI that makes it 100x better.
http://gamemusic.emugaming.com/The music to Tyrian, the greatest side scrolling shooting game of all time. Ok, it's in mp3, for some reason, and 2x faster than normal, but still kicks ass.
EDIT: Screwed up the Tyrian link, go find it yourself. Yes, it's worth it.
Overall, I find that MIDI tends to evoke sadness and nostalgia, for some reason. I'm not talking just about the old video games, either; the Metallica one shows this effect a lot. Also, at one time, MIDIs were seen as a major piracy issue, before mp3s.