Watch Shin Mazinger Z.
I'm a big big fan of Mecha, so keep that in mind.
Have you seen the second movie, Innocence? If not, watch it. It's good.
Ghost in the Shell - Movies and TV series are great.
Series or the first OVA + 2 movies? The first OVA and the 2 movies were directed by Mamoru Oshii, director of the Ghost in the Shell movies. Watch those if you haven't.
Patlabor - not bad, but not great, a bit slow maybe for my liking?
Another Oshii movie I'd like to recommend is Angel's Egg. It's great.
You could check out the series' that Miyazaki and Takahata made before the establishment of Ghibli. Future Boy Conan, Anne of Green Gables, Marco, etc. They're basically like Ghibli series.
I also like all of Studio Ghibli's stuff immensly but that's sort of a different category as I'm thinking about TV series here.
I also recommend their pre-Ghibli movies like Gauche the Cellist and Castle of Cagliostro. Also, if you haven't seen Only Yesterday (Ghibli movie unreleased in the US) I also recommend that. It's the best Ghibli movie.
I also just want to throw out a Redline recommendation, unrelated to any of the above. It's just awesome.