Actually owned... well that is a smaller list. I will go with things I had at the time rather than what I might have found since.
NES Tetris 2.
GB Tetris
GBC Zelda DX
GBA Minna No Soft Tetris
DS Tetris DS.
Master System. I actually liked the Master System Sonic.
PS1 Tony Hawk 2. Vagrant Story if I am allowed Tony Hawk 2 on another platform.
PS2 I really did actually like Final Fantasy 12.
PSP Tetris mini.
Gamecube. I liked several things but we still return to mario kart and smash on it.
Wii. For the 3 months I had one I guess I like Final Fantasy My life as king.
Sega CD. I only had Road Avenger.
Gamegear... I mainly used it as a portable master system but I did like columns on it.
Xbox, I will go with psychonauts actually. Failing that everybody liked the MX vs ATV game, in free roam it was pure relaxation the likes of which I have yet to find the equal of.
C64. Trying to decide between street surfer and toobin'
Can't be bothered trying to remember spectrum, amstrad or vic20 stuff.
BBC micro. It has elite. Elite TNK on DOS is my favourite but that is besides the point.
Amiga. Cannon Fodder if I am not allowed the DOS version, simulcra otherwise.
Dreamcast Skies of Arcadia
360, tough call but probably Resonance of Fate
Megadrive, has to be between streets of rage 2 and bomberman, I know PCE bomberman is better but eh.
N64. Bomberman 64. Yep, I said it. I might have considered perfect dark but it is unplayable now, like most N64 games are, but at least there is the XBLA version.
My brother owned a PS3 and there is also a PS4 now but the PS3 was basically the same as the 360, though for unique stuff for it then witch and the hundred knight which I reviewed I had a great time with. The PS4 has seen me take up battlefield 4 but that is hardly of any merit.
Otherwise have never actually owned a SNES, though I do like its version of Rampart, never owned a Saturn but its version of bomberman is fantastic, never actually owned a PCE/TG16 but I already mentioned bomberman for it, pong machine had pong and not a lot else.
PC. I quite like this internet game.