First up, I'm a huge fan of chiptunes and VGM in general, so my list might be a bit biased. Here goes however:
famousninja's Top 8 VGM themes (One game per franchise, all pre Windows '95. So no PSX either)
8: Skyroads - Intro (Blue Moon, PC) http://www.youtube.com/watch?v=b7yCVHni7uI
Brilliantly mellow yet driving and just very damn suitable for for what the game was, which was one of my most cherished memories as a child. (The odd beats in it are actually from the demo that normally plays in the background. Apologies)
7: Jazz Jackrabbit - Title Theme (Epic Megagames, PC) http://www.youtube.com/watch?v=mnnFFEStA3c
Brilliantly funky, and with just the right amount of sass, yet another theme that's ingrained into my memory from the many hours playing it.
6: One Must Fall 2097 0 Main Theme (Epic Megagames, PC) http://www.youtube.com/watch?v=gOShl4Tcw_E
Obviously inspired by trance and house music, this was another exceptional theme for another awesome game from the old Epic crew. There's hints of Rocky in there too. I'm sure that was deliberate.
5: Sam & Max Hit The Road - Pleasantly Understated Credit Sequence (LucasArts, PC) http://www.youtube.com/watch?v=4yWnnk9fyJE
This needs no description. My personal favourites out of all the LucasArts adventures. (The whole intro sequence is here because I fund it absolutely hilarious)
4: Top Gear - Track 1 (Kemco, SNES) http://www.youtube.com/watch?v=xpUZYWX2BoY
This theme was one of the reasons I got into electronic music, as well as making me want to learn guitar, so I could play this theme.
3: Doom - At Doom's Gate (E1M1) (iD Software, PC) http://www.youtube.com/watch?v=BSsfjHCFosw
I know that Bobby Price was ripping off Master of Puppets by Metallica. I know it's shameless. But this is BAD FREAKIN' Ass.
2: Donkey Kong Country - Jungle Groove (Rare, SNES) http://www.youtube.com/watch?v=uPTm-8YqJfw
Once again needs no explanation. Ingrained into memory.
1: Full Throttle - Legacy (LucasArts, PC) http://www.youtube.com/watch?v=7jx3Vz6cpXY
One of the first full digitised soundtracks in a PC Game. Without having to worry about size constraints due to these new CD fandangles, This was the first time I was gobsmacked at music in a video game. Damn good game too.
Please not this is my personal list. It is subjective, like everything in music. =D)
Also, to the OP: Red Dead Redemption isn't old. Either that or about ten years have past and I haven't noticed.