My sister just cleaned out their VHS closet, and I inherited a box of old anime tapes (which I specifically claimed!) So now I have the following series to watch:

Kimagure Orange Road
Bubblegum Crisis (and Bubblegum Crash)
Gunbuster
Appleseed and X-01 (seen both of these before)
The Hakkenden
Patlabor 1 (seen it, was pretty good)
Wings of Honnemaise (or something like that)

Most of these are pretty old... but classics like Appleseed are always fun to watch. The only series I would recommend to anybody is Cowboy Bebop.