I gotta lead off with one of my favorite things of all time - Robotech.
Surprisingly, I'm not a big anime watcher generally. But one day back in 1984, as a Junior in High School, I ran across this new show on TV, and I was hooked. I had watched the Transformers, and found it cheap and episodic. Then I saw the first episode of Robotech and the opening theme. I still get a thrill when I here the music:
Ironically, I missed both transition episodes that first run - and so I came back to the series the next day and all the characters were different.
What was different about Robotech (vs. US shows like Transformers) is that it was not episodic - each of the three series within it had its own story arc. In short, it treated its watchers like adults with an attention spam longer than 30 minutes. I used to have this poster of Rick Hunter on my bedroom wall:
When the DVD sets finally came out, it was a Godsend. I now own them all, and watch the series periodically.
If you've never seen it, I strongly recommend it. If you can get past Lisa Hayes' cinnamon bun hair: