Zillion is a very interesting "adventure platformer" game that's kind of a spiritual predecessor to the Metroidvania genre. (Or, perhaps more accurately, it's sort of an 8-bit Sega take on Metroid 1 specifically.) You control a character who descends into a maze-like underground facility and needs to collect notes that can be used to unlock new areas and items – while running and gunning against baddies, of course.
The game's password system is sort of its defining element – you need to carefully note and enter passwords to progress. There's no in-game record of the passwords, so you'll have to take them down on paper, which will stop some people from reading this right now. But I actually think it's quite a fun little mechanic that keeps you engaged in the "real world", and helps build a sense of intimacy and knowledge of the game world. It isn't so difficult that you're always having to die and restart, so you can really dig in and focus on code-cracking. Not for everyone, but I like it!
...And I also like it because it's based on one of my all-time favourite 80s anime,
Red Photon Zillion. (Which actually did get a few episodes released in the U.S. at the time!) The game is fanservice-heavy, with 8-bit renditions of the show's OP and ED themes on the plinky SMS sound chip, full-on character portraits for dialogue scenes, and the ability to play as all three major characters (with their own unique attributes, of course). It also has probably my favourite game over screen in any game, where the show's villain cackles at you. If you don't want to play it, at least do yourself a favour and listen to
this album on YouTube.
Alex Kidd in Miracle World, while not quite up to the level of the 8-bit Sonic games, is still a pretty console-defining game. It's easy to see why they were thinking of this kid as their mascot before Sonic came along – Alex Kidd is a very unique, unorthodox platformer that focuses on short-range attacking, item management, and some very charming and memorable boss battles.
It's short but kind of difficult for your first run-through, so you should get plenty of play out of it if you're up for a challenge. (Though be warned: you're not getting the best ending without a guide.) Much like Wonder Boy, the game also got a recent remake on modern consoles, but fans didn't seem to like it that much, and I think the redone graphics are kind of ugly. This is the best Alex Kidd game, so if you're at all interested in the franchise, check it out!!!!
The version of
Fantasy Zone on the SMS, much like the 8-bit Sonic games, is more of an adaptation of the original with several unique gameplay elements. It's probably the best console Fantasy Zone they made up until the excellent 3DS remakes, and if you like cute, cartoony spaceship shooters, I think you'll really enjoy it. Fantasy Zone is a great entry-level shoot 'em up, and it's fun even if you're not typically a fan of the genre.
If you like this,
Fantasy Zone II and
Fantasy Zone: The Maze are two other great SMS titles. (The latter is a really cool take on Pac-Man where you can shoot the enemies!) I'm a bit blinded by affection for the series when I write this, but the Fantasy Zone series is just so loveable that I really do think anyone can enjoy it, and I'd certainly recommend all the Master System games as a lot of fun.
Depending on how you feel about first-person dungeon-crawling JRPGs, the original
Phantasy Star might want to be on your radar. It's a very well-designed blobber that's heavily distinct from what was coming out on Nintendo consoles at the time – in addition to first-person dungeons, it also lets you interact with enemies in way, way more complicated ways than just attacking them. Why, you can even talk to them and make friends with them! They should make another RPG like that, and I should be allowed to strangle the developer.
Phantasy Star is a very important Sega game for an awful lot of reasons, but beyond all that it's just a darned good JRPG. I don't even like games like this, and I think it's really great. All the other Phantasy Star games are different to this one, so you'll be getting a very unique gameplay experience.
Psycho Fox is an oddball little platformer in the "pick up and throw stuff" category that also includes Kid Kool and Decap Attack. (All these games were made by the same company and are essentially reskins of one another.) It's not really the best game in the world, but these games do have quite the fanbase and are considered Sega classics by many.
For what it is, Psycho Fox is quite a cute, shallow platformer that's fun for a few sessions, and if you meld with the gameplay I certainly think it's worthwhile. Nice big chunky cartoon graphics, too.
Those are all the games that come to mind, but there may be others I post about later on. I love the SMS – it has loads of great games and an excellent audio-visual component that's sadly been pretty much forgotten by history. The Japanese version of the console also has an absolutely wonderful
startup sequence that I adore. All the other games mentioned in this thread are great, too, so you'll have lots to play beyond Sonic!