Metroid II: Samus Returns & Gargoyles Quest (such a bloody hard game) on the OG GameBoy were my favs. I played a lot of *Battletoads *on it too but that game was so bloody frustratingly difficult, especially for a kid, so played it mostly out of spite to get past the stupid brain ball chasing you level. Also loved Parodius (parody side scrolling SHUMP from Konami) but never owned it, so borrowed it from friends to play. Naturally I also played Tetris to the point that the music still haunts my dreams. There was also a pretty decent Spider-Man game for it, but can't remember it's name & it's not showing up on lists.

The OG GB also had a lot of bog awful licensed property (movie/tv/cartoon) tie in games too, as well as generally terrible releases. To see them all, check this list: https://en.wikipedia.org/wiki/List_of_Game_Boy_games

I unfortunately never owned an Advance, so only got into games on it later via official emulators (the Wii U control pad was the best GB Advance out there), so got to play Golden Sun later but enjoyed it as a fairly unique take on the J-RPG genre. The releases of Breath of Fire 1 & 2 on the Advance was also a great thing, since they were my favourite SNES games.

For GBA games, here's a list but so many shitty licensed games there too: https://en.wikipedia.org/wiki/List_of_Game_Boy_Advance_games