There are many types, depends what you like.
Generally rather good classic ones:
Patlabor, Wings of Honneamise, CyberCity/AD Police/GenoCyber trilogy, Black Magic M66, Bubblegum Crisis, Armitage III, Metropolis, Plastic Little
Ones that have done the rounds on TV, etc:
Tenchi Muyo Ryo Ohki, Mezzo, Fullmetal Alchemist, Cowboy Bebop, Love Hina, Great Teacher Onizuka, Dominion Tank Police, Louie the Rune Soldier, Ah My Goddess
Super Magic Girls:
Project A-Ko, All-Purpose Cultural Catgirl Nuku Nuku, Saber Marionette J, Moldiver, Gunbuster, Magical Girl Pretty Sammy
Girly: (school life, romance, magic fighting dollies)
Azumanga Daioh, Fruits Basket, Angelic Layer, Pretear
Cute Girl, Emotionless Killer:
Gunslinger Girl, Elfen Lied, Noir, Serial Experiments Lain, Kiddy Grade
Cute Girl that is actually a powerful robot masquerading as a maid:
Hand Maid May, Chobits, Mahoromatic, Amzing Nurse Nanako
Boyish: (robots, fighting)
Full Metal Panic, Tokyo Underground, Burn Up W/Excess, Green Green, Hyper Police, Inu Yasha, Kino's Journey, Ninja Scroll, You're Under Arrest
Fantasy: (historic, RPG-style)
Record of Lodoss War, The Herioc Legend of Ar(i)slan, dot Hack, King of Bandit Jing, Magic Shopping Arcade Abenobashi
Comedy, Quirky:
Excel Saga, Furi Kuri (FLCL), Ushio & Tora, KO Century Beast Warriors, Ranma 1/2, Di Gi Charat, Dragon Half, Ground Defense horse Mao-chan, Puni Puni Poemi, Slayers
And anything by Studio Ghibli, they are drawn with a more western style, but are great stories and the worlds created are amazing. Howl's Moving Castle is their best to date, Grave of the Fireflies was the one I've watched most recently, and was very moving.
There's also the horror, super-violent and porno ones, but I've never seen anything of very high quality, except the Ichi the Killer short, which somehow managed to be more violent than the live action version.
More info here:
http://www.animenewsnetwork.com/encyclopedia/anime.php