I will edit this list if somebody has additions.
Sega Saturn
Batsugun (J)
Battle Garegga (U)
DonPachi
DoDonPachi
Galactic Attack (U)
* aka Layer Section (J)
* aka Rayforce (E)
Gekirindan
Gunbird
Kyukyoku Tigers 2 Plus (Twin Cobra 2)
Shienryu
Sonic Wings Special
Strikers 1945
Strikers 1945 II
The Game Paradise
Gunsmoke
Image fight
Sega Dreamcast
Trizeal
Gunbird 2
Trigger heart Exelica
Under Defeat
Psyvariar 2
Ikaruga
Radirgy
Karous
Castle of Shikigami 2 (U)
* aka Shikigami No Shiro 2 (J)
Gunbird 2
Sony Playstation
Capcom Generations Vol. 1: 1942, 1943 Battle of Midway, 1943 Kai
Capcom Generations - Blazing Guns (E): Mercs, Commando, Gunsmoke
DoDonPachi
DonPachi
Raiden DX
Raiden Project
Sonic Wings Special
Strikers (only the imports have TATE, including the PS1 Book release)
Toaplan Shooting Battle (one game on there)
Twin Cobra
Xevious
Image Fight
Assault
Dragon Spirit
Exed Exes
Vulgus
Sony Playstation 2
Gunbird 1
Gunbird 2
Trigger heart Exelica (not yet released)
Psyvariar 2
Psyvariar Medum Unit
Psyvariar Revision
Radirgy
Dodonpachi Dai ou jou
Espgaluda
Mushihime sama
Ibara
Homura
Dragon Blaze
Raiden III
Shikigami No Shiro (Japanese version only)
Shikigami No Shiro II
XII Stag
Contra
Nintendo Gamecube
Ikaruga
Shikigami No Shiro II
Radirgy Generic
Nintendo Wii
Shikigami No Shiro III
Microsoft XBOX
Shikigami No Shiro
Shikigami No Shiro II
Psyvaria 2
Microsoft XBOX 360
Shikigami No Shiro III
Raiden Fighters Aces
I know, it's not much of a list (yet), but it's a start.
Update Thanks to some replies the list has grown a lot. Very usefull.

Update 2 Thanks to Kiken and others I added some XBOX and XBOX 360 Tate games.