Consoles :

Atari 5200 (1982)

Colecovision (1983)

Atari 2600 (1983)
Emerson Arcadia ("Galactica" clone, as "Space Attack")

Bally Astrocade ("Galactic Invasion")

Atari XEGS
Nintendo Famicom

Nintendo Famicom Disk (1990)

Nintendo Game Boy (1995, "Galaga & Galaxian")

Nintendo Game Boy (1996, "Namco Gallery Vol.2")

Sony PlayStation (1996, "Namco Museum Vol.3")

Sony PlayStation (1994, "Ridge Racer") : you can play the game while the main game loads.

Nintendo 64 (1999, "Namco Museum 64")

Sega Dreamcast (1999, "Namco Museum")

Sony PlayStation 2 (2001, "Namco Museum")

Nintendo GameCube (2002, "Namco Museum")

Microsoft XBOX (2002, "Namco Museum")

Sony PlayStation 2 (2005, "Namco Museum 50th Anniversary")

Microsoft XBOX (2005, "Namco Museum 50th Anniversary")

Nintendo GameCube (2005,"Namco Museum 50th Anniversary")

Sony PSP (2005, "Namco Museum Battle Collection")

Nintendo DS (2007, "Namco Museum DS")

Nintendo Wii (2007, "Namco Museum Remix")
Note : In the Korean version of Namco Museum Battle Collection for the Sony PSP, Galaxian goes by the name of 'Old Galaga', marking the only ever official connection between the Galaxian and Galaga series.
Computers :

Apple II (1980, "Galaxian" - Star Craft Tokyo)
Commodore Vic 20 (1981, "Star Battle" - Hal Laboratory)

Apple II (1981, "Alien Typhoon" - Star Craft)
Tandy Color Computer (1982, "Galax Attax")
Tandy Color Computer (1982, "Space Ambush")
BBC B (1982, "Arcadians" - Acornsoft)
Acorn Electron (1982, "Arcadians" - Acornsoft)
Sinclair ZX81 (1982, "ZX Galaxians" - Artic)
Atari 800 (1982)
Sinclair ZX Spectrum (1982, "Galaxian" - Artic)
Commodore C64 (1983, "Galaxions" - Solar Software)

Exidy Sorcerer
Sinclair ZX Spectrum (1983, "Galaxian" - Atarisoft)
Sinclair ZX Spectrum (1983, "Galactians" - DK'Tronics (UK))
PC [Booter] (1983)
PC [MS-DOS] (1983, "Galaxian" - Atarisoft)

MSX (1984)
Fujitsu FM-7 (1985)
Atari ST (1993, "Galaxian" - PD / Shareware - Sinister Developments)
PC [MS-DOS] (1997, "ChampGalaxia" - CHAMProgramming)
PC [MS-DOS] (1996, "Galaxi" - PD / Shareware - Kurt W. Dekker)

Commodore Amiga (1998, "Galaxians v1.3" - PD / Shareware - Kev Gallagher)
PC [MS Windows 95, 3.5''] (1995, "Microsoft Return of Arcade")
PC [MS Windows, CD-ROM] (2000, "Microsoft Return of Arcade 20th Anniversary")
PC [MS Windows, CD-ROM] (2005, "Namco Museum 50th Anniversary")
Others :
VFD tabletop game (1980, "Galaxian") released by Bandai.
VFD tabletop game (19??, "Moon Alien", alt. name) released by Bandai.
VFD tabletop game (19??, "Beam Galaxian", Japanese release) released by Bandai.
VFD handheld game (1981, "Galaxian 2", called Galaxian 2 because it can be a two-player game) by Entex (or Futuretronics).
VFD handheld game (1981, "Astro Galaxy", Japanese release) by Entex.
VFD handheld game (1981, "Astro Invader", Hales release) by Entex.
VFD tabletop game (1981) released by Coleco.
LCD Keychains handheld game (1997) released by Bandai.
Namco Classics TV Game (2003 - Jakk's Pacific)
Mobile Phones (2003, "Galaxian Mini")
Arcade Gold featuring Pac-Man (2007 - Jakks Pacific)
Retro Arcade featuring Pac-Man (2008 - Jakks Pacific)