A common misconception I come across is that anime is either Ghibli or cheap outsourced sometimes-the-characters-have-7-fingers BUT FRIEND LET ME TELL YOU that that is not the case!
Michael Areas, Hiroaki Ando
Girl Who Leapt Through Time / Summer Wars / Wolf Children: Ame and Yuki
Kaiba / Ping Pong the Animation / Mind Game
Ohayo / Paprika / Tokyo Godfathers
Garden of Words / 5 Centimeters Per Second
I actually don't watch a lot of anime so I'm not as well informed as I could be. Just know that I'm only skimming the surface!
Panty & Stocking / FLCL / Puella Magi Madoka Magica / Tatami Galaxy (also Yuasa heheheh oops!) / Mononoke / Cowboy Bebop
If you follow animators/story artists on social media, you probably know that anime is becoming a pretty big influence in the Western market- especially TV animation.
Revolutionary Girl Utena/Steven Universe
Utena isn't the only anime SU pays homage to but... too much effort to find all of the references haha..
we can't forget the new episode of Gravity Falls heheh..
In June, Adventure Time invited Masaki Yuasa (mentioned above) to direct/write/board an episode.
And uuuhhh... Avatar/Legend of Korra ????