The thing about the megadrive was that it had a LOT of fun 2-player games:
EA Hockey was great; BODY CHECK B*****S!!!
Micro machines (All of them) are great fun.
Streets of Rage 2 was awesome; 1 and 3 were a bit crap IMHO.
World of Illusion was surprisingly fun despite being a Disney game

Single player platform game of note include Taz, Quack Shot, Chuck Rock (I always loved the intro music

) all fun platformers but are beaten by Earthworm Jim 1 and 2; They're he ones to get if you can!
Rocket Knight Adventures and Sparkster (RKA2) are also excellent, although the SNES versions benefited from the extra buttons.
If you can find a copy of Zero the Kamikaze Squirrel, that's a great and very underrated platform-beat-em-up

JRPGs, the only two I remember being any good were the Shining Force and Phantasy Star series, but I don't think I ever completed them (Weren't a patch on the SNES' Chrono Trigger.)
Jungle Strike and Desert Strike are megadrive classics too, but avoid Urban Strike, which was pants.
Ecco the Dolphin was a beautiful game but HARD AS F*****G NAILS. I blame it for my dislike of dolphins. I never played 2 because was traumatized by 1 (The whole game is pure evil but the last level is PURE EVIL ON A STICK MADE OF EVIL WITH A COATING OF EVIL SAUCE* (*made of evil))
For beat-em-ups, I will say the Mortal Kombat series was much better on the megadrive than Street Fighter. The SNES had the better Street Fighter conversions.
But I will say this: If you buy nothing else, the one game you *HAVE* TO GET is Gunstar Heros.
It is bar none the best run-and-gun shooter ever made! And it's *two* player!!!