Millennial, 1993. I remember Sega/sonic, Pokemon yellow/blue, Digimon (first season), Legend of Zelda Orcarina of time & Majora's Mask, FFVII-IX being really big when I was a kid. We also had this gray Nintendo, but we had traded it for Nintendo 64. I think Nintendo 64 (Sega and PS1, too) was more prevalent for my childhood, but the gray one was probably more so for my siblings (they're 5-10 years older).
Some people naysay things like this on forums but I understand the curiosity xD It's pretty interesting (and weirdly fun to see the variety /squints/ I expected mostly Z's and millennials. So, when the first post was like I'm Gen X," I was all "oh, that's cool

" because it wasn't what I expected. xD
On a side note, my babyboomer dad was actually the one to get me into games. They were mostly PC games and I'd usually play those whenever he brought me into work for a little bit (this was like... when I was toddler or something). He was actually the one who got me into Final Fantasy in the first place, too xD Before I could even read, he, my bro, and I had played FFIX together and it was so much fun. He or my bro would take turns reading the dialogue for me in a very animated way. It was a lot of fun.
You're a millennial, most likely :3 Generations usually span about 20 years (give or take a couple).