These are my personal favorites. Note that many of these I enjoyed as a kid so I can't 100% be certain adults will like all of them lol. Some of these are also pretty popular so you may have heard of them already.
NES: Lone Ranger, Super Mario Bros 2, Spy vs Spy
SNES: Earthbound, Pilotwings, Blackthorne, Super Mario World 2: Yoshi's Island, Kirby Superstar
N64: Super Smash Bros, Star Fox 64, Paper Mario
SMS: Didn't play this one much.
Sega CD: Lunar: Silver Star
Sega 32X: Knuckles' Chaotix, but I'm fairly certain it would not be great as an adult.
Sega Saturn: Didn't play this one much either. I remember thinking Nights into Dreams looked really pretty but it felt pretty unrefined, and didn't get into it.
Sega Dreamcast: Only every played Crazy Taxi on this one.
Neo-Geo: Never played it.
PS1: I liked a game called Dragonseeds. FF7 and FF9, and FFT too. Harvest Moon: BTN.
Game Boy / Game Boy Color: Zelda Link's Awakening (DX), Pokemon Games, TMNT: Fall of Foot Clan
GBA: Final Fantasy Tactics Advance, Moto Racer, Mario Kart Super Circuit
DS: Final Fantasy Tactics A2, Mario Kart DS, Professor Layton Series, Phoenix Wright Series
PSP: I didn't ever have one, or emulate one. But if the Sid Meier's Pirates port is any good, it may be worth a shot!
If possible, update us on how the Retroid Flip is!