Love love love this topic:) I used to be really into art and thought I even wanted to be a concept artist--that didn't work out but I'm perfectly happy with it--and anyway I will very often watch an anime solely because the art is beautiful or different.
Actually, I don't think any art styles
turn me off, even if they're slightly dated, but I do get frustrated when the animation and production are low-quality. Pretty much everything is beautiful when the characters aren't moving, but a low budget can botch a lot of things, haha.
Oh, but I am sensitive to CGI and more hesitant to watch it though not totally opposed.
Some of my personal favorites:
I love the beauty in all of the small details for The Garden of Words
. Ghibli especially animates rain beautifully--I felt this way when I was watching The Secret World of Arrietty too.No Game No Life
was a lot of things, but it did
have one of my favorite color palettes.
That watercolor background in Grimgar of Fantasy and Ash
No one mentioned Katanagatari
yet but I know this show is popular for its unusual (and deceptively simple) art.Yuri on Ice!
hasn't even aired yet but LOOK AT IT THE FLUIDITY IS STUNNING I AM MADLY IN LOVE
and seriously there is going to be a winter sports anime which is so exciting I hope it's beautiful agggghhhhhhhh....
Looking at what I posted it seems I actually have a preference for really sleek art or really sketchy art. Interesting.