I view myself as a child of the 90's. I was born in 1980, but I came of age and "grew up" in the 90's. The music and movies of the 90's still resonate with me more than anything that is created now because it recalls the times when I was growing up, hanging out with friends- moving from childhood into manhood.
The major events of that decade- the death of Kurt Cobain, Columbine, etc can be recalled still with great detail.
I still owe a lot of musical tastes and fashion to the 90's as well, and I always look back on that decade with fondness.
That's what it means to be a child of a decade, IMHO.