The 'Saturday Anime' programming block on the Sci-Fi Channel back in the mid-90s. Granted, I couldn't watch much of it, but every so often I would. After that my interest tapered off for a while until Toonami started (early 1997), and I watched Voltron and Robotech. That got me back into it a little, although I was extremely into Robotech, and after the huge buzz over Dragonball Z and Gundam Wing faded out around late 2000, I lost interest again until mid 2002. It was mainly AMVs (the ones usually considered classics - Engel, Right Now Someone Is Reading This Title, that one Pokémon video that I'm not going to repeat the name of here, etc.) that I found scattered about on peer-to-peer networks - those got me to remember some shows that I'd heard about but never watched. So that lead to me watching Oh My Goddess! (OVA) and Neon Genesis Evangelion* that summer. I've not lost interest since. Mid-2002 was also when I first started editing AMVs, using only VirtualDub (that was painful - I moved onto Premiere in 2003).
*Interestingly enough, when I was into Robotech we'd go to Barnes and Noble and I'd get the novelizations of the series. This was ~1998, and then, like today, they had the graphic novels/manga in the subsection of the Sci-Fi area where the Robotech novels were. I distinctly remember picking up the Eva manga and flipping through it, and thinking to myself, "I'd like to get this", but I wasn't about to pay - or ask my mom to pay - 15 bucks for a book as thin as those were. Several years later I ended up getting them (vols.1-7 in the old left-to-right large bound version).