These are most of the games I had that I recommend.
All Sonic games.
All Streets of Rage.
All Shinobi.
Ecco.
Cool Spot.
Toejam and Earl.
Golden Axe 1 and 2
Battletoads
Lethal enforcers
Marko's Magic Football
Alex Kidd
Mega Bomberman
Castle of Illusion (Mickey Mouse)
Quackshot
Fantasia
Flicky
Lemmings series
Moon Walker (Michael Jackson)
Aladdin
The Jungle Book
The Lion King
Alien Storm
Desert Strike
Urban Strike
Chuck Rock
The Double Dragon series
Dynamite heady
James Pond (the others suck..... more)
Krusty's Super Funhouse
Tazmania
There's also another game that rocked.. I don't remember much about it or it's name, but you threw hotdogs at someone and went on a skateboard across town and roller blades.. It was an awesome game, if anyone remembers what it was called, let me know.
Edit: They look LIKE hotdogs, they probably aren't.. But sometimes you get a super flying hotdog thing that protects you from baddies.. Anyone?
EDIT: YES!! Greendog!
Greendog is a cool California surfer that decides to wear a cursed pendant he finds on the beach. However, the pendant will not come off, dooms the wearer to be attacked by animals and prohibits surfing. The only way that Greendog can lift the curse is to travel to lost Aztec civilization and track down six pieces of a lost treasure. The single-player gameplay requires you to survive several side-scrolling levels, armed with only a flying disc that you can shoot at enemies to destroy them or at various objects in order to gain more energy.
The game had some homages to earlier side-scrolling adventure games, such as Pitfall as the character often had to swing on vines to advance and many of the levels take place in a tropical jungle or in an ancient temple. Many levels required the player to use a skateboard or rollerblades to advance.
At the end of each level, Greendog must defeat a boss in order to obtain a piece of the treasure. After defeating the final boss, Greendog returns to the California beaches to surf and hook up with a beautiful young woman.
I'd say that looks like a hotdog.