My first foray into anime was with Pokemon back in '99. But I've loved DBZ, Gundam (Seen most of them), Yu Yu Hakusho, Rurouni Kenshin, Outlaw Star, Last Exile, Naruto, Black Lagoon, SAO, Knights of Sidonia. I was a kid when Toonami was playing on weekdays on Cartoon Network. I was definitely a 90's kid to remember the golden age of cartoon network. So there were tons more shows I could list and name.
I've also recently gotten into slice of life anime like Usagi Drop, Toradora!, and Your Lie in April, as well as Chihayafuru.
What turns me away from certain anime are the overuse of anime expressions. I can't stand One Piece and Soul Eater for this reason.