1992... I knew about Super Mario Kart, but after some research, I found out some other great games, like Sonic the Hedgehog 2, Mortal Kombat, Batman Returns (SNES), Alisia Dragoon and Darkwing Duck (NES).

Doing some "research" in Wikipedia, I found a game created in my birthday year that could be good as an answer to this thread. It's not a series, however, but it fits me so well that I can't help but posting it here. It's this one.

=P

1985 - Super Mario Bros.

nuff said

1978... Space Invaders, which was the biggest video game in history up to that point.

Space Invaders

Pokemon

Oh, nevermind

I'm not proud of that

Age of Empires. 

Not necessarily proud of it (because why would I be proud for a video game series), but I am glad the second game still has such a great following, it's a testament to its greatness. 

Pretty much nothing to pick from that I'd care about from that far back.  /chuckle

Mostly just board games back then.

https://en.wikipedia.org/wiki/1977_in_video_games

1977 was the first Zork-game, a great series that defined adventures for a long time:

https://en.wikipedia.org/wiki/Category:1977_video_games

Some games were released in my birth year, but none of them made it into a series.