PS1: No idea since I didn't get one until ~'97/'98 and played it at a friend's house prior. When I got one, it was one of whatever my brother and I got. Crash Bandicoot 3, Small Soldiers (lol), or something.
PS2: Summoner. Despite the shit this game got, I loved it, save for the ridiculous load screens.
PS3: MGS4.
PS4: Dragon Age Inquisition.
PSP: Played a friend's, and have no idea. When I got one, it was Ys Seven.
Vita: Katamari.
PS5: Should be Demon's Souls if my pre-order comes through.