Arc the Lad I and II
Suikogaiden Vol.1 and 2
Hybrids (Part 2D and Part 3D, like Xenogears or Grandia):
Arc the Lad III
Basically dithering is used to hide the "banding", or low end color gradation which was typical in video games of that era, low color gradation can be observed on low color depth screen for example (though not as noticeable), see 8 bit screen vs 10 bit screen:

The 10 bit screen has superior color gradiation than the 8 bit screen.
Dithering can be used to hide low end color gradation, see:

On the left you can clearly see banding in the horizon, while on the right side you don't see it as it's being cleverly hidden by the dithering.
However, dithering is pretty much useless for 2D games and only serve to add a grainy nature to the picture, see:


But for hybrid games, games such as Arc The Lad III, Xenogears, Grandia etc., mainly games that use 2d characters mixed in a 3D polygonal environement, dithering also seem to have it's uses, as it once again cover the low end color gradation (compare the floor):
