Nowdays for a mobile Tetris option i'm using a SNES emulator on my phone (Snes9x EX) and Super Tetris.
Meanwhile, there are companies creating on the web and mobile app versions of Tetris, inserting ads and charging money for what should be free.
Link's Awakening is my favorite Zelda game.
The original Pokemon games (Red/Blue, Gold/Silver) that others are recommending are pretty rough these days, but it's fun to see where it all started if you have the patience for them.
If you want something a little less well-known, Bubble Ghost is a fun little puzzler.
Regardless of what you try, remember that this is the era when game manuals were required reading since they rarely were able to fit tutorials & instructions in-game. It's good to scan through the manual first before you play something or you might be missing some critical information.
Game Boy games tended to be limited due to space constraints.
Link's Awakening feels like it shouldn't be possible in a single megabyte of mask ROM, for example. The fact that it was makes it almost more impressive by today's standards.
I feel like I don't really encounter stories of heroics in making games work on their hardware anymore. Even at the end of PS1 with Final Fantasy their hand drawn backgrounds were too big to fit into VRAM iirc
Or in the PS2 era Jak and Daxter using the principle of hot reloading from lisp to figure out open worlds without loading screens
Half a megabyte, even! (For the original monochrome game - the later color version is a full megabyte.)
Pokemon is actually a really difficult game before modern QOL. No DLC!
Wario Land 3 is a really really good Game Boy Color game.