Rockin' Kats (I thought this game was exceedignly awesome when I was a kid. not sure if it still holds up, be I'm sure its worth checking out)
Battle City
Mighty Bomb Jack
Spartan X (a little short, but its a classic... I think...)
And of course some classics (thought not all good) to find the origin of popular Nintendo characters
Ice climbers
Donkey Kong 1
Donkey Kong 2
Super Mario Bros. (the arcade game, not the side-scroller)
Wrecking crew (one of the weirdest mario games)
Kid Icarus
And Wild Gunman if you want a better understanding of the arcade scene in Back to the Future 2
Battle City
Mighty Bomb Jack
Spartan X (a little short, but its a classic... I think...)
And of course some classics (thought not all good) to find the origin of popular Nintendo characters
Ice climbers
Donkey Kong 1
Donkey Kong 2
Super Mario Bros. (the arcade game, not the side-scroller)
Wrecking crew (one of the weirdest mario games)
Kid Icarus
And Wild Gunman if you want a better understanding of the arcade scene in Back to the Future 2