My first ever anime was Inuyasha, I believe. I was like five or six years old while it was airing on Adult Swim, and I stay up late to watch it because I loved the action scenes and music for the opening / ending.
The first anime I watched knowing it was called "anime", it was Skip Beat!. Still love it to this day.
But, the actual first anime I watched was Pokemon.
Rosario to Vampire. Thanks to imageboards I started watching anime with subs, unlike the most other newbies. I was so excited and delighted that I can't explain, but now I understand how shitty this title is.