Oh man! I know I’m going to miss some really good production studios and anime, but here it goes:
I’ve loved pretty much every series that P.A. Works has come out with (True Tears, Angel Beats, Hanasaku Iroha, and Canaan).
You can’t leave out Kyoto Animation, with The Melancholy of Haruhi Suzumiya, Nichijou, K-ON!, Clannad, Clannad ~ After Story, and Kanon.
I love the work of Shaft, which produced Bakemonogatari, Sayonara Zetsubou Sensei, Puella Magi Madoka Magica, and Arakawa Under the Bridge.
I’ve loved a lot of Genco’s work too - Azumanga Daioh, Elfen Lied, and Honey and Clover.
Manglobe has had some really good success too with Samurai Champloo, Ergo Proxy, and Deadman Wonderland.
Studio DEEN has some great shows too, like Zipang, Shonen Onmyouji, Fate/Stay Night and one of my all-time favs, Seitokai no Ichizon.
There’s also Madhouse, which has so many works under its belt: Black Lagoon, Tokyo Godfathers, Claymore, Gunslinger Girls, The Girl Who Leapt Through Time, and Summer Wars … and about 100 more. LOL
You can’t leave out Studio Ghibli, which produced Hayao Miyazaki’s work - Princess Mononoke, Spirited Away, and so many more awesome movies, as well as other works, like Grave of the Fireflies (a beautiful and utterly depressing movie).
I don’t know who produced them, but I loved the movies 5 Centimeters per Second, Voices of a Distant Star, and The Place Promised in our Early Days, all of which were by Makoto Shinkai.
I know I’ve missed some, but these are some of the first anime that popped into my mind as my favorites.