For games that I recommend, you can try the titles of Dragon Spirit, Galaga '90, Bomberman, Bomberman '93, Super Star Soldier, New Adventure Island, Air Zonk, and Aero Blasters (those titles are at the top of my priority to have, and are considered, for the most part, to be excellent games to have for the system). Other titles you can try are Psychosis, Splatterhouse, Pac-Land (if the port is decent to play), J.J. and Jeff (a big maybe, however), Space Harrier, and Takin' It to the Hoop. Some others can mention titles that work for you, as well, since I determine these from the best of my knowledge and preferences.
If you also have or plan to recieve a CD add-on to a TurboGrafx-16 or a TurboDuo system, then you can also try the games of Lords of Thunder, Gate of Thunder, Wonderboy: Monster Lair, Fighting Street (you may need to endure rough controls, though), Super Air Zonk, Shadow of the Beast, and Exile. Again, these are only my personal preferences, and others can mention more that are good for you.