I'm gifting my friend's child a handheld emulator and loading it up with games. It's capable of playing things pretty much up to Nintendo GameCube (It's even running Twilight Princess, though it studders in some areas).
I've got pretty much everything that exists for NES, SNES, N64, as well as a couple dozen games for Genesis. I never had a Sega Saturn or a PS / PS2 growing up though and I'm wondering what I should grab for those, as well as some more obscure GameCube titles if there are any I should know about.
Here's your chance to wax nostalgic about some old games and help ensure they make it into a kid's present. Even if I have the game already, I can still throw suggestions into the "favorites" list and make them easier to find.
Yes, there are so many good games for GBA and even GBC and they're small so you can go for the whole library approach like NES/SNES.
I don't know that much about the Playstation, having also never had one growing up, but the top shelf classics that come immediately to mind are Final Fantasy VII and Castlevania: Symphony of the Night. There are also tons of kid friendly mascot platformers like Crash and Spyro
Even the original GB had bangers, like Donkey Kong '94
The original Pokemon R/B/Y games were technically GB games, even though Yellow did do some colors if you played it on a GBC. Metroid 2 was also a GB game.
Link's Awakening, too, but the DX version was a little better
Edit: Totally forgot about Kaeru no tame no Kane wo Naru "For the Frog the Bell Tolls" - it's a strange Japan-only GB game that's roughly a more puzzle based Link's Awakening. There's a fan translation out for it.