Once your Wii is connected to the 'net, go to the Wii Shop Channel in the Wii Virtual Console and you'll find it full of classic console games that download to your system for a fee.
Games include titles from the SEGA Genesis, TurboGrafx-16, TurboGrafx-CD, Neo-Geo, Nintendo Entertainment System, Super Nintendo and the Nintendo 64. To play these games you'll need a GameCube controller or a Wii Classic Controller.
Below are titles A through F.
For more games check out Part 2 - Titles G through Z.
Alien Soldier
Original Platform: SEGA GenesisPublisher: SEGA
Developer: Treasure
Original Release Date: 1995
ESRB Rating: E+10 for Everyone 10 and older
Alien Storm
Original Platform: SEGA GenesisPublisher: SEGA
Developer: SEGA
Original Release Date: 1991
ESRB Rating: E+10 for Everyone 10 and older
Altered Beast
Original Platform: SEGA Genesis/Mega DrivePublisher: SEGA
Developer: SEGA
Original Release Date: 08/1989
ESRB Rating: E for Everyone
Art of Fighting
Original Platform: Neo-GeoPublisher: SNK Playmore
Developer: SNK Playmore
Original Release Date: 12/11/1992
ESRB Rating: T for Teen
Art of Fighting 2
Original Platform: Neo GeoPublisher: D4 Enterprise
Developer: SNK
Original Release Date: 1994
ESRB Rating: T for Teen
Axelay
Original Platform: Super NintendoPublisher: Konami
Developer: Konami
Original Release Date: 9/1992
ESRB Rating: E for Everyone
Balloon Fight
Original Platform: Nintendo Entertainment SystemPublisher: Nintendo
Developer: Nintendo
Original Release Date: 6/1986
ESRB Rating: E for Everyone
Baseball
Original Platform: Nintendo Entertainment SystemPublisher: Nintendo
Developer: Nintendo
Original Release Date: 10/1985
ESRB Rating: E for Everyone
Baseball Stars 2
Original Platform: Neo-GeoPublisher: D4 Enterprise
Developer: SNK Playmore
Original Release Date: 04/28/1992
ESRB Rating: E for Everyone
Bases Loaded
Original Platform: Nintendo Entertainment SystemPublisher: Jaleco
Developer: TOSE
Original Release Date: 07/1988
ESRB Rating: E for Everyone

