The Many Genres of Anime  by Jareth David
(originally written as a study guide for tour guides for the My Reality exhibit.
This is an expanded version of the flyer I wrote for the Tampa Museum of Art.)

As the subtitling company ADV likes to say, “Anime is a medium, NOT a genre”. Just about any genre you’ve seen in Hollywood films or TV has had numerous anime series or films in Japan which have been released in the U.S. (You can find links to information about these titles at AnimeMetro.com)

Note: many of these titles can be described by more than one genre or theme
This list is just a quick basic guideline and by no means even vaguely complete:

Action  (Cowboy Bebop, City Hunter, Lupin III)
Children’s shows (Pokemon, Doraemon)
Magical Girls (Sailor Moon, Card Captor Sakura, Minky Momo, Nurse Angel Lilika S.O.S., Pretear)
Savior from another Dimension (Vision of Escaflowne, Fushigi Yuugi, Magic Knight Rayearth, El-Hazard, Orguss, Heaven War Shurato, Record of 12 Countries [12 Kokuki])
Hero (Gatchaman, Hurricane Polymar, Casshan, Hakaima Sadamitsu)
Sci-Fi (Evangelion, Dirty Pair, Wings of Honneamise, Rah Xephon)
Space Opera (Gundam, Macross, Xabungle, The Ideon)
Fantasy (Record of Lodoss War, Slayers, Aura Battler Dunbine)
Military/ Police (Full Metal Panic! , You're Under Arrest [Taihou Shichauzo], Patlabor)
War (Grave of the Fireflies, Area 88)
Samurai/ Ninja (Rurouni Kenshin, Ninja Scroll [Juubei Nimpucho], The Samurai)
Martial Arts/ Fighting (Dragonball Z, Saiyuki, HunterXHunter)
Ghostbusting (Yu Yu Hakushou, Haunted Junction, Ghost Sweeper Mikami)
Comedy (Ranma ½, Urusei Yatsura, Dragon Half, Excel Saga)
Romantic Comedy/ Soap Opera (Kima