Finally some Ranma 1/2 appreciation because that was my first completed series and probably one of the biggest contributor to my love for anime today.
Though in my country the most influential during my generation would be Dragon Ball, Sailor Moon, Slam Dunk, Yu yu Hakusho, Flame of Recca, Gundam Series, Doraemon, Pokemon and Fushigi Yuugi.
I started watching it in the 90's when Viz was releasing it on VHS, with just two episodes per tape, at like $25 each. And I had like 20 or more tapes (I got a deal on some of them, at least).
Anime fans today don't know how good they have it :)