>>314991When it comes to series Nichijou and Dennou Coil are often said to have the best animation on a tv-anime. Then there's stuff like Space Dandy, Mob Psycho 100 that for a tv-series handle animated motion exceedingly well for the whole run.
Stuff like FMA:B, Moribito or Cowboy Bebop and Samurai Champloo have great fights. For more subdued animation that is distinctively high quality you could look for example at Hyouka and Mushishi.
For unique and/or interesting art, though not necessarily always technically amazing animation, check for example Masaaki Yuasa's productions, studio Shaft (take this with a grain of salt though), Gankutsuou, Mononoke, Big O etc. There's a lot and not too hard to find really.
Really though, movies consistently have higher quality animation than tv-series so if you want the best you should look into those more.
Old home-video boom era OVAs also have often really great animation because companies just threw money at studios to make what the fuck ever as long as there was a moderate prospect for it to be rented. Look for 80's, early 90's stuff.