I've always liked media with anthro characters, but my introduction to the furry community was actually at an anime convention.
I had preordered my tickets for A-kon 2002, and back in the day when you preordered you got a few little comic books from a local comic book store in your bag for free. As fate would have it, one of my free comics was Havoc Inc #2. I stayed up late that night reading and rereading the comic, and then trying to draw the characters. I loved it.
A-kon 2002 came and went (great con) and I started setting my sights on what I wanted to cosplay as for A-kon 2003. That summer, Hamtaro had started airing on Cartoon Network, and I thought it would be funny to make a big mascot-suit style costume of Hamtaro. So I googled "how to make a mascot suit" and one of the very first pages I ran into was Yappy Slyfox's webpage, The Fox Den. After that, there was no escape.
Really cute!