Setup WinUAE and try and get AmigaOS 3.9 on it. It is fun to play around with. Plus you can install games to the virtual HDD.
Some good Amiga games.
Super Skidmarks 2
Super Cars II
I mention Amiga because back in the day it usually had the superior version to multi-platform games.
Detective - Amazing game for its time.
The Simpsons Arcade Game
Teenage Mutant Ninja Turtles Arcade Game 1,2
Marvel Vs Capcom
Alex Kidd In Miracle World
Mickey Mouse Castle of Illusion
The Lion King
Super Mario RPG
Super Mario Allstars + Super Mario World
I was a C64 and Amiga child so i can't recommend any more console games.