I can give you a few games and scenarios off the top of my head:
Donkey Kong Country - SNES
The gradients in the green Nintendo Logo. I like them to gradually fade to black without crushing the darker tones.
Similarly the speakers in the boom box, I like to be able to see the speakers without raising the black levels.
Super Metroid - SNES
Blend dithering on the letters on the Title Screen.
Super Mario World - SNES
Blend checkerboard dithering on blue background and water.
Super Double Dragon, Final Fantasy Mystic Quest, Samurai Showdown
Make sure power bars are rendered evenly.
This also applies to the level meters in Ninja Spirit - Turbo Duo’s sound test.
Some of these can be resolved, helped by choosing the correct aspect ratio and scaling settings.
Gate of Thunder 4 in 1 - Turbo Duo
When Bonk appears, make sure you can see darker shade of yellow is visible in the center of the spotlight without there being a harsh/obvious transition between the 2 shades.
Gate of Thunder Intro, Ys IV cut scenes, Psychosis level 1
Blend all dithering to produce additional colours without introducing any NTSC artifacts to ruin the illusion of seamless additional colours.
Lords Of Thunder, Bank’s Revenge
White text in HUD can be used to test highlight clipping.
Genesis:
Well everyone know about Sonic The Hedgehog level 1 and Streets of Rage 2 bar level for checking transparency and the rainbow effect but Sonic 2 Chemical Plant Zone is a good one too.
Sega Saturn:
Daytona USA for transparencies
PlayStation:
Marvel Super Heroes, Shuma Gorath in the title screen for testing saturation/clipping.