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.
![Tongue :P](./images/smilies/tongue.gif)
Oh, but I am sensitive to CGI and more hesitant to watch it though not totally opposed.
Some of my personal favorites:
![Image](http://img2.goodfon.su/wallpaper/big/8/b8/art-makoto-shinkai-kotonoha-3239.jpg)
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.
![Image](https://s-media-cache-ak0.pinimg.com/736x/5f/5a/91/5f5a91142b435d2140106cea051bb806.jpg)
That watercolor background in
Grimgar of Fantasy and Ash though.
![Image](https://3.bp.blogspot.com/-4yUHyrKKKPQ/VglK7YT-a6I/AAAAAAAACEM/K57BivVM7A8/s640/205029.jpg)
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.