I honestly remember being maybe about five and playing in the living room with my sister while my dad was watching TNG and wondering how anybody could possibly watch anything so hideously boring.
I think the episode I remember is Ensign Ro, but maybe it's just wishful thinking. All I really remember for sure is Picard and his gleaming pate(this was, incidentally, before my dad starting shaving his head...).
I got into Voyager when I was about 16 because I was looking for femslashable TV and thought J/7 was intriguing. It was, but I also fell in love with the whole feel and concept of it. So the first full episode I remember watching is Caretaker.