I'm new, and I know there is an official topic to present myself, but I prefer to answer this.
I saw the topic creator permits 32X and Mega CD games there, so, as a fan of 32X, I will do a "deep" 32X game recommendations:
32X
Excellent and Notable games in 3D:
1-Virtua Fighter: A late release in 32X life. I have an special love for this version. New modes included, and all the amazing animations and moves of the original, in a little cart of only 4MBs (32Mbits). The models are even more "blockier" than arcade and Saturn versions, but this part of its charm. The original tunes are here, and has good voices. Very very amazing port... amd, for what I know, almost got cancelled. It seems Sega America people saved it. Oh, and NO loading times unlike the ones in the Saturn version. So, this game is not only a curiosity, is a real contender as the best Virtua Fighter 1 version.
2-Virtua Racing Deluxe: A launch title, and a must play if you like the series: 2 new type of cars, 2 new circuits, all made by the creators of the original game. Virtua Racing Deluxe was, until the launch of Ridge Racer and Daytona USA for the home market around mid/late 1995, the BEST racing game you could had in a domestic console, period.
3-Stellar Assault/Shadow Squadron: An exclusive 3D space shooter. Very underrated game, even in its day. 2 Modes of play and you have the possibility of a coop with a second player. Is a VERY NICE an polished exclusive game for 32X. Music is very 16Bit (not an outstanding one, but nice), but the graphics and gameplay is the deal here. It had a sequel for Saturn in Japan, totally ignored by the general public until some years ago.
4-Star Wars Arcade: Notable conversion of the Model 1 game, made with little resources and time. A very arcade Star Wars game, like the name says. Difficult and really fun. Impressive in 1994.
Excellent and Notable games in 2D
1-Space Harrier: a fantastic native port of the arcade version from the 80s. You also have "After Burner Complete" for 32X, a fantastic port if you like After Burner. But I don't that much).
-None other: The rest of 2D game are not THAT good to make you want a 32X. Some, in fact, are just bad or even have better versions in Sega CD/Mega-CD.
Not THAT good, but interesting games to try, in 3D:
-Metal Head: probably the best 3D full-textured game for the 32X, being those very rare in 32X. 3D games in 32X used basically polygons with plain colors. This game is the only one I would REALLY recommend in this "interesting" list. Almost almost went to the upper one.
There is an easy secret code to convert the characters who speak with you, to an anime-style girls. Normally, I'm not a very fan of those kind of things... but in this case, I recommend to check it out. You lose the recorded voices, but it truly deserve it a try, because they are more likeable than just seeing a bunch of 40 to 60 year old guys speaking to you all the game. Somewhat, the game experience changes.
-Zaxxon Motherbase 2000/Motherbase/Parasquad: Every region had a different name for the game. A shooter. Basically a polygonal isometric 3D Zaxxon, but with new interesting mechanics, made by CRI, the sister company of SEGA when both were subsidiaries of CSK. A decent, difficult and exclusive game.
-FIFA 96: A PAL exclusive. This FIFA season had LOOOTS of versions for many many consoles. 32X also got one, and it is its only soccer game. Is a 3D game with 2D sprite players. Some kind of a "cheaper" version of FIFA 96 for Saturn and PSX. Like the rest of FIFAs, lots of National Leagues and competitions, and also many national teams. It was interesting in its day, because it was like the MD version, but with a 3D component in the gameplay, including different cameras! "oh my Gwad".
-Darxide: A PAL exclusive. A 3D space shooter, fully textured. It was one of the last releases. The console suffers a lot to move its mission intros and closing sequences in real time (3-5 fps). Also, it is very very repetitive. But it's just fine as a simple arcade game, like an "Asteroids" from 1979, but in textured 3D. The gameplay is a lot smoother than the intros, but in the end, is just a "meh" game in general. It has some kind of a cult by some, but In my opinion, does not deserve it. Copies are now insanely expensive, because almost nobody in Europe buyed that, at the end of the 32X commercial life.
(Apart from those, you can now find fan versions of Doom which are extremely good in 32X (Doom Resurection for example. There is also a Doom 64 version for 32X which needs some recognition). But I DO NOT recomment the original Doom released for 32X: is a half-baked version, and the music is just too mediocre or even bad.
Not THAT good, but interesting ones to try, in 2D:
-Kolibri: a nice "bio" shooter made by the same people of Ecco the Dolphin. Nice and relatively innovative idea. OK.
-Mortal Kombat II: "they" say it is a VERY good conversion from the arcade, but... it is just MK2. MK3 and its sequels were better, so... only for 2D fight-loving gamers. Curiously, Sega CD had an excellent MK1 port, so... I don't know... cool, I suppose. Both, 1 and 2, were also released in normal Genesis/MD with inferior ports... but Genesis got MK3 and Ultimate MK3, better games in the end.
-Tempo: a colorful childish platformer. It had a sequel for Saturn. Don't expect a miracle, but it is fine. Has not PAL version and US and Japanese ones do not work in a PAL machine, being software locked.
-And what about the famous "Knuckles' Chaotix", the only "Sonic" game in 32X?
Like Sonic CD in Sega CD, it was the reason every child wanted a 32X.
Well, it depends on the user. I do not like that game and I do not recommend it. I think it is a boring experience with no real meaning, and the game is too long for what it offers (barely nothing). The stages are not that well designed, they are colorful and full of "details" but sometimes is very difficult to understand what can be "used" or not as a path, and the new mechanic (2 characters united with an elastic rope) is a very irregular one to be the real core of the gameplay:
Chaotix has some nice ideas, but in the end every level have 5 stages (too many) and none of those levels are really memorable... except, maybe, the first one (that's because they are all TOO colorful and saturated of details: all the levels resemble too much.
It has, though, an interesting 3D special stages, not very polished, but enough fun to be interesting. By the way, the bad ending is hilarious: absolute craziness... making your efforts to beat the game totally useless or even catastrophic, in a major manner. And the good end? 100% unsubstantial.
GENESIS/MD
-Sonic 2D platforming games (Especially 1 and 3. The last one, separated from S&K because the different music, but Sonic 3 and Knuckles is the complete game, so, go for that)
-Virtua Racing (an amazing piece of technology for the 16bit. Of course, inferior to the 32X version).
-Super Hang-On (FANTASTIC game. Arcade and Original modes, both are great. Original mode is especially made for the home console and is a "Career mode". I prefer this home console game than the Arcade one).
-Shining Force 2 (1 and Shining in the Darkness are also good, but 2 is better)
-NHL Hockey series (any of them with fights, total fun. Much better than 16 bit FIFAs)
-Streets of Rage series (SoR2 above the others).
-Ninja Turtles: Hyperstone (great beat 'em up)
-Columns (the FIRST one, phenomenally classy, inspired in the phoenicians, with a beautiful soundtrack. NOT Columns III, very very meh. The second one? never appeared in the console).
-MUSHA (Amazing vertical shooter from Aleste series. 10/10 OST)
-Comix Zone (fantastic beat 'em up, and very artistic).
-Sonic Spinball (I don't know why I love this game and its 8bit adaptation. It pretended to be a bridge between the -by then- new Sonic animated series, and the games. Its OST is as abrasive as a genesis game soundtrack can be, but I simply love its tunes).
-Flashback (this is what now cheap people call "a Metroidvania", because "Adventure Platformer" is less cool. Good story, good gameplay, and excellent animations).
-Any Treasure Company game (pure 68000 gasoline for your Genesis/MD)
Sega CD/Mega-CD
-Road Avenger
-Shining Force CD
-Final Fight CD
-Lunar series (both)
-Thunderhawk
-Mansion of Hidden Souls/Yumemi Mistery Mansion (is a fever dream experience)
-Snatcher
-Sonic CD (a very special classic Sonic, but a lovely one, with a Sonic 1 feeling and art style. And alternative Sonic 2)
I do not really recommend any "32X CD" combo game: they are just FMV games, also available in Sega CD format.