I think I'll do games while I was alive! I did play some older games too when I was a kid, but nothing older than Pac-Man I think.
1982 -
Digdug - MADMAX
1983 -
Mario Bros. - I would say Dragon's Lair as well but I've never actually played it.
1984 -
BoulderDash - I only just now got the pun, hahaha, but I owned this on NES!
1985 -
Super Mario Bros. - My first videogame, I got it from my Grandma & Grandpa, my Mother was worried I was being spoiled and videogames would wreck my life...she was right!
I like many others pressed up instead of A and died on the first Goomba and immediately raged, good times. I didn't get it when it was new, though.
Hang-On - Even if the bikes were super loose by the time I played this game, it was still really exciting

1986 -
The Legend of Zelda - I played this so, so much. I had the gold cart, a cool Nintendo strategy guide, everything. Why oh why did I sell it and my NES?
Out-Run - The music is so memorable, and I still play it to this day! I also used to get free rides on the deluxe moving cabinet at my Mum's old work, I'm pretty sure I was reunited with the cabinet this year at a gaming expo I went to, but they lowered the timer so it was impossible to get past level 2
Metroid - Didn't actually play it through until later in life though.
1987 -
After Burner 1 & 2 - That rotating cockpit <3 but it did suck money from you because it was not an easy game at all

I even played the R360 version once, which literally empties your pockets by turning you upside down. The music is also sexy as hell.
Megaman - I didn't own it or beat it when it was out, but later I did. (with save states because it's SO HARD)
Double Dragon - my friends and I would just play VS mode because the graphic were better, pick Abobo and run at full speed into each other, over and over.
Street Fighter - I played this in the 90's around the time when SF2 came out, it still had the huge punch button you had to actually punch! ... I think I may have played this because all the SF2 machines were busy

1988 -
Megaman 2 - best music, best Megaman!!
Super Mario 2 - I got this for Christmas one year, I was so happy
Double Dragon II - I don't think I ever finished this one either, but yes, it's the best one
Chase HQ - This is Nancy at Chase Headquarters, I played this on Amiga or Atari ST I think, I played it in 2016 at a retro arcade in Tokyo, it was great!
1989 -
Final Fight - An all time classic and I wish I had played it in the arcades, but I never saw it around for some reason? The SNES version is good! but it's crippled sadly.
Teenage Mutant Ninja Turtles Arcade - I loved this so much, as a kid the cabinet looked HUGE and 4 people could play at once, it was when the cartoon show was huge and the movie was coming out..aaaaaa. the game itself was crazy with great graphics, effects and everything. PIZZA TIME
Teenage Mutant Hero Turtles NES - This is possibly the worst game ever but I still foolishly plugged away at it because I loved the turtles and thought I could beat the game one day (I never could)
Tetris (Game Boy) - I got this with my Gameboy I think, still the best one

I'll do the 90's later!