Sega Genesis/Mega Drive for you foreigners

[AlliSabbah]

Buck Rogers

Shadowrun

Some pirate game by the people that do Romance of the three kingdoms was pretty fun but its been so long I forget the name.

[WhiteRat]

Any of the Strike games, specifically Desert Strike. Also check out Mutant League Football. Any game that features Bones Jackson and let's you play football on an asteroid should be worth a look.

[Girl Drink Drunk]

Sidescrollers:
Shinobi III
Bonanza Bros.
Sonic the Hedgehog 3
Toe Jam and Earl: Panic on Funkotron
Jurrasic Park
Robocop Vrs the Terminator
Alladin
Rocket Knight Adventures and Sparkster
Spider-Man vrs the King Pin
Moonwalker
World of Illusion
Ristar
X-Men 2
B.O.B
Ghostbusters
Castlevania Bloodlines

Puzzle/Adventure:
Lemmings
Dune
Out of this World

Beat em ups:
Streets of Rage 2
TMNT: Hyperstone Heist
Battle Toads
Splatterhouse 2 & 3

RPGs:
Shining Force

Other:
Lethal Enforcers
Zero Tolerance
Truxton
Worms

Games like Dune, Out of this World, Zero Tolerance, and Lethal Enforcers may or may not be your thing so you might want to a few out on an emulator first, but otherwise, you'll probably like the other mentioned games.