• SNES

  • the Donkey Kong Country trilogy, just good platformers; first one hasn’t aged as well as people think, if you don’t enjoy it skip ahead to 2 and come back later if you feel like it
  • The Lost Vikings 1 and 2, fantastic character-switching co-operative (but playable solo) level-based puzzle-platformer; don’t play the sequel on newer platforms like PlayStation, they tried to modernize the graphics and only succeeded in making them hideous, stick with SNES
  • Star Fox 2, as long as you enjoy dated 3D and poor framerates, this is the most ambitious 3D game on any 16-bit console, with a very replayable campaign full of hidden unlockables that differs on each play
  • Super Mario All-Stars & Super Mario World, just an enhanced compilation of 4-5 seminal 2D platformers; while you could use save states on the NES versions, the SNES versions all support native saves, so easier to pick up and play
  • Tetris Attack, nothing to do with Tetris, just a match-three puzzler with deep, engrossing mechanics that can keep you interested long-term; also Panel de Pon with a translation hack if you want more
  • Top Gear, fantastic competitive racer with the line-scroll road effect you know from classic arcade games like OutRun and a killer soundtrack; pick the white car
  • Yoshi’s Island, another classic platformer

• Mega Drive/Genesis

  • Gauntlet IV, better than the arcade original, this is M2 (now known for developing emulators for many classic systems) flexing with some RPG mechanics added to the traditional Gauntlet gameplay
  • The Lost Vikings, SNES version is better but there’s a few brand new levels in this one if you want more
  • Sonic the Hedgehog 3 & Knuckles, basically the first Sonic that noticed it’s a home game, so it has saving and improved replayability with multiple characters, paths and unlockables

• Game Boy

  • Donkey Kong, this is not a port of arcade Donkey Kong, it’s a full-blown puzzle platformer you can play one level at a time
  • Kirby’s Dream Land 2, easy-to-finish platformer but with tons of content if you’re playing “properly”, using the sort of rock-paper-scissors logic to use the right powers to enter the secret areas
  • Super Mario Land 2: 6 Golden Coins, just a proper “mid-period” (SNES-esque) Mario platformer which you can play over as long as you like

• Game Boy Color

  • Balloon Fight GB, predates Flappy Bird by literal decades but like if that was a proper game with a campaign
  • The Mummy, based on the Brendan Fraser movie and an awesome Konami puzzle-platformer with short individual levels and password save (use save states on emulator), super underrated
  • Pokémon Puzzle Challenge, Tetris Attack but with Pokémon if you prefer that theming
  • Wendy: Every Witch Way, based on some kind of comic book I think, developed by WayForward who developed the Shantae games and then branched off into Yacht Club Games (Shovel Knight), Wendy is a gravity-flipping platformer where you’re in control of which direction is up or down

• Game Boy Advance

  • Advance Wars 1 & 2, adorable turn-based strategy war game with a campaign based around small, self-contained levels, except for a few huge ones
  • Drill Dozer, developed by Game Freak (Pokémon), is a sort of level-based Metroidvania platformer with lots of backtracking to older levels as you unlock new abilities
  • F-Zero: Maximum Velocity, the only true sequel to SNES F-Zero, don’t at me
  • Game Boy Advance Video: Shrek, endlessly replayable
  • Metroid: Fusion and Zero Mission, they’re Metroid games
  • Super Mario Advance 4: Super Mario Bros. 3 e-Reader version, I think you can get this officially on Switch somehow, but you’ve been to the Internet before; this officially-released modified version of the original game includes a bunch of brand new levels previously distributed only on scannable cards, I’m not telling the whole story but they remix elements from the first four mainline Mario games into basically a whole original game. This is New Super Mario Bros. this is Super Mario Bros. 5, still don’t at me

Adding Android too because many of those are quite old and are also quite portable (with most being officially distributed as APKs, which I guess adds up to how old they are).

#hasicontent (PICO-8)
Anodyne (Android)
Atari Vault’s selection if you got it before it was delisted (Atari 2600, Atari 5200, Atari arcade systems)
Augury Red Code (GBC)
BlazBlue: Continuum Shift Extended (PSP)
Böbl (NES)
Bolt (PS2) - if on Android, use AetherSX2
Bravely Default (3DS)
Castlevania: Symphony of the Night (PS1)
Celeste Classic (PICO-8)
Celeste Classic 2 (PICO-8)
Codemancer (Android)
Crisis Core -Final Fantasy VII- (PSP)
Dandara: Trials of Fear Edition (Android)
Devil May Cry (PS2)
Devil May Cry 3: Special Edition (PS2)
Dissidia 012 Final Fantasy (PSP)
Downwell (Android)
Dragon Ball: Budokai Tenkaichi 2 (PS2)
Dusk Child (PICO-8)
Dust: An Elysian Tail (iOS)
Ever Oasis (3DS)
Final Fantasy II (PSP version specifically)
Final Fantasy VI (SNES, PS1, GBA, Android)
Final Fantasy VII (PS1)
Final Fantasy XII / Final Fantasy XII: IJZS (same story, different gameplay mechanics) (PS2)
Final Fantasy XII: Revenant Wings (sequel of FFXII) (NDS)
God Hand (PS2)
God of War and God of War II (PS2)
God of War: Chain of Olympus (PSP)
Godzilla: Unleashed (PS2)
GrimGrimoire (PS2)
Gunbird (PS1, PS2, arcade)
ICO (PS2)
Ittle Dew (Android)
Lost In Dungeon (Android)
LYNE (Android)
Metal Slug and Metal Slug 3 (the ones I played) (Neo Geo)
Micro Mages (NES)
Naruto Shippuden: Ultimate Ninja 3, 4 and 5 (PS2)
Naruto: Uzumaki Chronicles 2 (PS2)
Nix: The Paradox Relic (NES)
Odin Sphere (PS2)
Okami (PS2)
Parasite Eve (PS1)
Persona 3 FES (PS2)
Phoenotopia (Adobe Flash)
Quest of Dungeon (Android)
Shadow of the Colossus (PS2)
Shantae (GBC with a small optional part that needs to be played in the GBA)
Shantae and the Pirate’s Curse (3DS)
Slay the Spire (Android)
Slayers (SNES) (use accuracy-oriented emulators, though, since speed-oriented ones like Snes9x glitch the saving feature)
Slipways Classic (PICO-8)
Solatorobo (NDS)
Sonic Mega Collection Plus (PS2) or even the titles included in it (and/or SEGA Mega Drive and Genesis Classics from Steam) through Mega Drive and Game Gear emulators
Tallowmere (Android)
Tanglewood (Mega Drive)
The Fairly OddParents! Shadow Showdown (PS2)
The Simpsons Game (PS2, PSP)
The Simpsons: Hit & Run (PS2)
Unchained Blades (PSP, 3DS)
Va-11 Hall-A: Cyberpunk Bartender Action (Android using an unofficial wrapper)
War of the Monsters (PS2)
Wishing Sarah (sequel of Dreaming Sarah, a PC game) (Game Boy)
Wonder Boy in Monster World (Mega Drive)
コテ・DE・メクール (PC-9801)
真・魔王ゴルベリアス　先取り横スクロール面 (PC-9801)

• Puzzle Games
  • Super Puzzle Fighter 2 Turbo (GBA, other platforms)
  • Puzzle League (GBA, paired with Dr Mario same cart)
• Roguelikes
  • Dragon Crystal (Sega Master System, GG too)
  • Shiren the Wanderer (Nintendo DS, others too)

I find puzzle & roguelikes the best for just diving in for a little bit and not worrying about when you drop off.

Puzzle Quest
Bejeweled
Peggle
Plants vs Zombies
Punch Out
Pokemon Mystery Dungeon

Mr Driller
Chu Chu Rocket
Meteos
Polarium
Honeycomb Beat
Super Monkey Ball

off the top of my head.

heh, I could probably just list my whole DS collection (minus all the JRPGs and proper weird strange stuff like ElectroPlankton).