Well dependent on what kind of genre you like here are a few i can think of:
Shonen: One Piece, Hunter x Hunter, My Hero Academia, One Punch Man
Romance: Ouran High School Host Club, Uta No Prince Sama, Chobits, Love Live!
LGBT: Sekai Ichi Hatsukoi(gay), NO. 6(gay), Sweet Blue Flowers(lesbian), Junjo Romantica (gay)
Slice Of Life: Cowboy Bebop, Free!, Clannad, Toradora!, Suzumiya Haruhi no Yuuutsu, K-On!
Others i recommend: Fullmetal Alchemist, Haikyuu!!, Mushishi, JoJo no Kimyou na Bouken, Hellsing, Welcome to the NHK, Samurai Champloo, Fate/Zero, Psycho-Pass, Angel Beats!
Hopefully this list helps !
Is it me or does Cowboy Bebop being classified as slice of life just seem wrong?
No, it's not just you... that's not right at all.