A lot of games in this era had their anime style box art redone for the American market, usually with hilarious or terrible results. These games have very Japanese style graphics, even if the box art might not look like it. The Valis and Lunar games are great too.
King's Knight (NES)
El Viento (Genesis)
Faria: A World of Mystery and Danger (NES)
The Krion Conquest (NES)
Popful Mail (Sega CD) (this game is absolute catnip for someone looking for games like this!)
Magical Drop III (Neo Geo)