I'm gonna try to just name one game from each system:
NES: Wizardry I - This is the perfect port of Wizardry. It has updated graphics and an origional soundtrack (unlike basically all other versions of Wiz I). Further it doesn't leave anything out that was in the PC version. The only way it could have been more perfect would have been if it had some of the Wiz I expansions accessable once you beat the main game. I easly put 1000 hours of my life into this title on the NES alone. To hide it from my religious zealot parents I put Wiz inside a Golf cart shell which I purchased at a used game store for about 5 dollars.
PC-Engine: HuVideo - Can an old 8bit processor handle passable FMV? Oh yes it can. Oh yes it can. I am simply impressed the PC-Engine can do this at all.
Gameboy: Final Fantasy Legend I - Another great hour killer. It has a brutal leveling system involving nothing more than millions of hours of gold earning to buy stat increase potions while you travel up a tower and visit other worlds. It also had great graphics for the time and has a wonderful soundrack.
Genesis: Gain Ground - I simply love playing the unforgiving bitch 2 player. Who ever heard of a game so brutal it is a special ability practically to shoot in any direction but up? On top of it, once you get hit once, by anything you not only die, but loose that character unless you can rescue their body with another character before time runs out. On yeah, and you have a time limit, so you cannot just wait to take every perfect shot.
SNES: Street Fighter II: Turbo - Again, another port that makes my head spin it is so good. I don't know if it is the most faithful home port of this game, but I suspect it is. The voice samples sound very good. The action is smooth and fast. I remember some background animation missing, but that is probably because of a lack of power and space on the SNES. On top of all of this, to this day I still believe this is the ultimate fighting game. There is just so much right about SFII: Turbo and so very little to complain about.
Virtual Boy - Red Alarm: Red Alarm is a wonderful 3D vector shooter. The fact that it is on the Virtual Boy makes the 3D impressive, not gimmicky. The sound track is as alright as any first gen VB game and the sound effects are not unpleasant.
PC-FX: Zenki - I don't think there is anything more I can say about Zenki that I haven't already. Simply the best FX game hands down.
Sega-CD: Silpheed - A very graphically impressive game for it's time, and a good port of the PC-88 game Silpheed.
CDI: none - the CDI deserves to be burried with ET. No game can be good on the CDI.
Jaguar: Tempest 2000 - I must admit this is the only game I give a stale fart about on the Jaguar. Sorry baby, but I just have not been too impressed with your cart games I have played.
3DO: Starblade - The most perfect version of Starblade assuming you do not own the dual LD arcade version. If you own that, you are a far better fan than I. Starblade though is one of my all time favorite rail shooters...this comming from a person who loves railshooters. The 3DO version has faithful voice to the arcade version and the graphics are only worse in a few places like when your ship launches (because LD FMV is replaced with 3DO FMV). A must own if you have a 3DO.
PS1: Vib Ribbon - In a vector side-scroller, populated by one lone inhabitant "Crack-Rabbit", who must navigate through the dangers of your own personal CD collection, this is one of the few PS1 games I am SHOCKED there is not a special PSP version of. The Vectrex could have handled the graphics, but does that matter? No. Crack Rabbit is simply one of the best games ever developed and is a wonderful party game.
DC: Ikaruga - One of the best shooters of all time. In Ikaruga, you can change yourself to either black or white like Michael Jackson. If you are white, white bullets and
people enemies will not harm you. Your white bullets while they will harm a white enemy a little, if you change to black and hit a white enemy with black bullets, it will die much faster. There is a real skill to being able to switch your color correctly every time. Again, great graphics and sound.
Xbox: Shenmue 2 - Free Shenmue 1 video disc, no disc swapping, works wonderfully from HD for the ultimate shenmue experience, English as well, which for this game series is a must.
PS2: Fatal Frame 1 - The most creepy survival horror game ever made. Never to be re-produced as well. Play this baby at night with the lights off and the sound up. Basically you are trapped in a Japanese mansion for whatever reason, the only thing standing between you and the gates of hell is a camera. Full of depraved FMV scenes and creepy twisted Japanese rituals, this game will keep you squirming the whole way through.

Gamecube: Resident Evil 4 - After years of stale RE games, the finally had the balls to re-think the genre. Instead of being a hunt and fetch puzzle game, it is much more a FPS game. Zombies work together to stop you, the bosses are actually a tiny bit challenging at times. It was new lifeblood the series badly needed.
DS: DS wars, the 2nd one - It's just a very solid "wars" title. The multiplayer mode is great, even if you just have 1 DS. If you have multiple DSs, I find it most fun to play seperate games on each one. You pass the DSs around and you have to try to win multiple games at once.
PSP: Every Extend Extra - My favorite puzzle game of all time. You play a mine, you goal is to blow up as many things as you can at once. If you blow up enough things, you get more mines! Combined with a rockin' tracker soundtrack, there is no way to go wrong with this game.
Xbox 360: Rez - Why Rez on the 360? Because Rez is proof that even the 360 cannot screw up the best game of ALL time.
PS3: I have not looked into this system much.