I already posted a suggestion in the 90s thread, but I have two possibilities for this one.
In the late-80s and early-90s, a lot of significant game franchises got their own cartoons (Mario, Sonic, Donkey Kong, Mega Man and several others). However, there are a few that never made it to the small screen.
One relatively obscure option would be 'Dr Chaos', originally released for the NES. The basic premise is that you play the brother of a Mad Scientist (the titular 'Dr Chaos'), one who experiments with Warp Zones in his huge Mansion.
Okay, so there's not much of a story to it, but that never got in the way of any of these animated versions (the Super Mario Brothers Super Show comes abruptly to mind). I could honestly see this coming out as something ultimately silly, but fun to watch.
The other suggestions comes from Sega, and was one of the most popular arcade racing games of the late-80s.
'Out Run: The Animated Series'
Let's see... we've got fast cars, tropical beaches, varied locations... just create some characters, add a gang of rival racers and the occasional 'saving the day during a race' plot, and you're all set.
Actually, I've just thought of another one (which may or may not have been already mentioned) - 'After Burner: The Animated Series'.
I'm thinking 'Swat Kats' meets, I don't know, 'GI Joe' or 'The Centurions' or something.