Simply put, this is the finest example of the genre you will find on any platform, home or arcade, to date.
Cyberbots: Fullmetal Madness
Although it's not Capcom's best work, it's a near perfect translation of the Japanese arcade version.
Puyo Puyo 2
Connect falling puyos to clear them away and dump filler on your opponent's screen before your screen fills up.
Lunar 2: Eternal Blue
Those with a tolerance or desire for older games and the nostalgia inherent in them will definitely want to give Lunar 2 a shot.