Twinkle Star Sprites (InstanceTopic, 15)
From Compile Worlds
Twinkle Star Sprites is a shmup/puzzle game for the arcade systems Neo Geo, Dreamcast, and Sega Saturn developed by ADK.
The story involves amateur witch Arle Nadja Load Ran, and her sidekick Carbuncle Rabicat trying to stop Satan-sama Mevious from stealing the Twinkle Star, which grants people one wish. However, other people also want to get the Twinkle Star, such as dragon rider Draco Centauros Realy Til, who wants to sing well, Schezo Wegey Arthur Shmitt, who wants to marry Load Ran, and so on.
The gameplay involves two playfields, which are separated by a vertical bar. Enemies appear on each side of their respective players' screen. Each player has to shoot these enemies so they can send fireballs/garbage into their opponents screen. If you shoot enough enemies, you can do special attacks, and even send out a boss(!!) to the opponent. Which is always a moment of pure win.
Oh, and its also really, really fun. Seriously, even if you're just skimming through random articles, you have to give this game a try. Its incredibly seizure-rific, and fun.
It's even been imitated by Touhou! See Phantasmagoria of Dim.Dream and Phantasmagoria of Flower View. Heck, even its sister series imitated it!