First one really was Space Cruiser Yamato. Ages ago, I had it on Tape Cassette.
Then the normal TV stuff, Sailor Moon, Pokemon, DBZ.
I kinda got into real anime last year because my flatmate had a huge collection. The first one I saw was Beck. After a bit of a discussion with another friend, he said that the series Chobits was just for girls. After watching the series and thoroughly enjoying it I concluded that pretty much anyone can like Chobits.
I have since seen classic stuff like Evangelion, Berserk, Full Metal Alchemist Brotherhood and up to episode 70 of Bleach.