I thought I'd give a few thoughts on each in order I saw them (I've already picked out my top TV Show/Film on the other thread).
Wolf Children (2012)
I caught this on TV when SYFY (I think) showed a load of Madhouse produced films before returning here mid-2017. Although Ghibli released 5 films last decade, of which The Tale of Princess Kaguya is my favourite (although Film4 "aired" them all so I could have picked Princess Mononoke for this list
), it was Hosoda's tale of coming to terms with who you want to be that beat them all as one my favourites of the decade. It contains some great moments both storywise with a range of emotions and animation wise.
Anohana (2011)
In the Spring of 2017 after a friend told me about Your Name. I searched for it online and came across a different film called Anthem of the Heart (
on YouTube 
) which for some reason I watched anyway and I loved it (it just missed out on this list). Fast forward to later that year, I was back on here and AotH was my first Anime Limited purchase. I was also now on MAL and decided to look for other stuff by the writer/director team and came across Gundam:IBO (which also missed out) and AnoHana which became one of my first import purchases.
A moving show about coming to terms with lose and being able to let go and move on with your life. Its varied cast all had their own coping mechanisms, but only by coming together and talking through what had happened can they truly find their way.
Monthly Girls' Nozaki-kun (2014)
In my first half year here I mainly focused on watching older stuff that I had missed out on. I was going to put Mushishi here, but when checking the dates of the 2 seasons we've had so far I realised that season 1 was 2005! 9 years before season 2 in 2014! (season 3 in 2023 please
) and felt that they really should go together and as I didn't have a comedy show on my list I'd go for Nozaki-kun.
This was an hilarious rom-com that hasn't been beaten by any of the comedies I've seen since.
I started watching seasonal anime in Winter 2018 and hit the jackpot straight away with not one, but two excellent shows:
Yuru Camp (2018)
On the face of it a show about girls going camping doesn't sound like an interesting idea, but this show has so much to it with its varied characters, comedy and infotainment. The artwork especially the backgrounds are really nice and the animation adds to the characters with some fun actions.
A Place Further Than the Universe (2018)
This show is almost perfect in every aspect. Characters, comedy, drama, art, animation and music all come together to tell a story both uplifting and moving in equal measure.
Sound! Euphonium (2015/6)
Musical based shows came down to this or Your Lie in April and felt this was more consistently great episode to episode.
After APFTTU finished I again looked for shows by the writer and/or director and this was one of them.
A school club show without all the usual tropes of finding members/advisor and of underdogs making it to nationals. Instead it concentrated on what it is that makes people want to persue (or not) their passion and the drama of trying to get into a band that already has high standards and the relationships that gets forged under that pressure. It also has some lovely art and some great animated moments.
Kill La Kill (2013)
After watching Gurren Laggan this was on my PTW/Netflix list, along with Little Witch Academia (a Trigger property that just missed out on the best list), until I learned it was leaving the platform.
An off the wall comedy about a girl wanting revenge and paroding the hierarchy of the school system builds and builds to a crescendo that tackles weightier topics.
Art and animation are top notch in every scene from the smallest stuff to the most outrageously over the top fight scenes.
Mob Psycho 100 (2016/2019)
Of all the shows that had multiple entries, but only part of it scored a 9 this one got a spot due to the fact that the second season is so good that it elevates the series as a whole that little bit more unlike say Psycho Pass as the second season was a downward step!
The story of a boy who's psychic power is so strong he can level buildings, but would rather be normal and make friends the regular old way and works hard to improve the aspects of his life that aren't so strong. Numerous characters would probably be bad guys if it wasn't for the affect of having Mob in their life,
indeed some were before they met him. Has some funny moments and epic scenes with a unique art style and excellent animation.
Fruits Basket: First Season (2019)
As re-adaptations go it's up there with Fullmetal Alchemist: Brotherhood (I'm not sure you can count it as this decade, but if did of course that would be on the list).
This was much better than the first attempt with a bit less of the slapstick stuff and upped the emotional moments. The art was also better.
PROMARE (2019)
As I said when I watched it, it's the Imaishi/Nakashima (GL/KLK) formula shrunk down to 2 hours! Complete with the same insane art and animation, and a great soundtrack.
Hopes the OP doesn't realise my ulterior motive for setting it out like I did 
