We were lucky, a friend of our parents owned all the rental 'video games' on the island (here in Guernsey). These were the type you used to put 10p in to play them and they were common place in bars, arcades and hotels. This friend first loaned/gave us a proper 'tabletop' version of 'Asteroids', hence I became brilliant at it because we had it for months and never needed to put any money into it, and then later he swapped it for us so we could have PacMan instead (I also got very good at this). Ultimately the PacMan tabletop 'died', and the friend gave us permission to donate it to a local charity in case they could fix and sell it. No idea if they did or not! Essentially we 'owned' both games at the point we had them as he would never have asked for them back.
The first game I ever owned was for the black and white Nintendo GameBoy (I got it after the color versions came out thus making it affordable) and that was Zelda. I wouldn't own another system until two years ago when I agreed to get the Wii (ironically another Nintendo system).
The first game i ever owned is The Sudden attack. Its a shooting game. i love to play it.After this game in 2011 i didn't purchase any other game.But i think i purchase a new game for my palystation 3 soon.
I honestly can't remember which SNES game was our first/we got with system when we bought it. Maybe Ken Griffy Jr. Homerun Derby? I do know we've had Tetris Attacks (the Mario one) for what seemed eons.