Quantum Leap (original). It was about a year after it had finished, and reruns were being aired on USA and SciFi. I was 14 and was immediately hooked. It's still my favorite show to this day.
Buffy the Vampire Slayer. I was the perfect age for it, but for some reason I never watched it when it originally aired. I started watching it when it showed up on Netflix, and had to binge watch the entire series in 2017 before the license expired. Loved it and wished I would have watched it sooner.
I Love Lucy, if that counts. The ultimate feel-good classic that I've been watching for my entire life.