These are all JP boxart, but they were all released in the west too.
Wardner - Ghouls & Ghosts-like arcade conversion platformer, can be hard, but fun, very under-rated because of the underwhelming visuals
Marvel Land - Namco theme park themed platform arcade conversion - lots of variety in levels (rollercoaster, Janken bosses like Alex Kidd), lots of shortcuts and secrets, and look out for the Namco character cameos (personal favourite of mine this one)
Gain Ground - Unqieu top-down puzzle/shooter with light strategy elements, you rescue new characters who you can then use, they all have different weapons/abilities.
Burning Force - nice little Space Harrier clone from Namco
DJ Boy - Kind of hard, frustrating but fun scrolling beat 'em up, arcade conversation
Elemental Master - Top-down shooter from Technosoft (Thunderforce series),
amazing soundtrack!
Ghostbusters - Fun Mega Man-like platformer
Magical Hat Adventure - Cool platformer, very similar to Pyscho Fox on Master System, reskinned and released in west as Decap Attack
Devil Crash/Crush - Cool pinball game, nice graphics, horror theme and great music,
Rolling Thunder 2 - Classic Namco platformer, Shinobi-esque
(Sword Of) Vermillion - Decent RPG, not as good as Phantasy Star or Shining Force series' though but I really enjoyed it as a kid, it was my first RPG I think.
Toki / Ju Ju Densetsu - Monkey platformer, arcade conversion
Wonder Boy V: Monster World 3 - Must buy platform/action RPG.
Hellfire - Nice space shooter, decent music
Crackdown - Arcade conversion, top-down puzzle/shooter - charge bombs and get out before the timer counts down.