Gunbuster is the
anime that made
Gainax famous. Before
Nadia, before
the Wings of Honneamise, before
Evangelion, there was
Gunbuster, "Aim for the Top!".
Gunbuster alternates between a neat hard sci-fi flavor and a sometimes-silly "giant robots" flavor. Relativistic effects figure heavily in the story, particularly time dialation, and the bad guys are like something out of an E. E. "Doc" Smith novel. Really quite cool.
However, the show's namesake, the "Gunbuster" (what does it do? Bust guns?) which is (bet you didn't see this coming) humanity's last hope against the alien menace, is clearly an homage to the campy giant robot shows that were so common in 1970s Japan. Gunbuster itself was animated in 1988.
The noted character designer Haruhiko Mikimoto did the character designs, and it shows -- the characters have a significantly different look from any of Gainax's other titles, helping make Gunbuster more memorable still.
Noriko Sakai sang the opening theme, and it can be found on Rhino Record's The Best of Anime compilation CD.
The series really transcends its genre's conventions at the end, and even now when I watch it I find myself shedding a tear - it's that good. It was directed by Hideaki Anno, so how could it be anything but epic? He is indeed one of the best directors the human race can lay claim to.