I doubt I'll be able to keep this up for thirty days, what with everything else going on, but I'll do this first one, at least.
To be honest, I don't remember the very first anime I ever saw; it was probably either Speed Racer or Kimba, which used to be syndicated on DC's Channel 20, an independent station that had a lot of cheesy syndicated stuff. I also didn't really think of Space Cruiser Yamato (a/k/a Star Blazers) as anime, probably because back then I'd never heard the word, much less heard about the genre.
The first time I ever saw anime as anime was thanks to the late therevdrnye and his friend Charles G., who was an otaku before being otaku was a recognized alternative lifestyle. They insisted on showing me some of Miyazaki's Castle In The Sky, My Neighbor Totoro and Kiki's Delivery Service, along with a taste of Dragon Half and Gunsmith Cats. That was pretty much all it took to hook me, and after I showed my kids the copies of Totoro and Kiki, they were hooked too. The rest, as they say, is history.
Honorable mention goes to Ranma 1/2 and All Purpose Cultural Catgirl Nuku Nuku; I don't know which one of these I dragged home as a rental first, but they both helped set the hook in me.