Thankfully my list at the top isn't as crowded yet so I can name them all, though they are more than 10.
This is in no particular order, each of them is great in their own way and all of them are extremely unique.
Kill La Kill
A testament of what anime can be besides 2D moving pictures. An action masterpiece with lots of twists, amazing animation, music and direction. It's directed by Anime God Hiroyuki Imaishi(Gurren Lagann, FLCL, Evangelion) so you know that the action will start the first episode at 100% and will only go up from there until a phenomenal ending.
Azumanga Daioh
Surreal, deadpan, dry, crazy, fast, slow, cute, funny. In my opinion the best comedy anime ever made, rivaled only by a very few. Forget Nichijou or Lucky Star. This is the true king.
Grave of the Fireflies
Gut-wrenching is the word that comes to mind here. A classic war drama about WW2 and its consequences in Japan. There is no fun here, only suffering. It highlights not the horrors of war but the horrors that will eventually result from it. It is focused on a young boy trying to care for his little sister. Turns out it's not that easy in a country ravaged by war. The conclusion will leave no dry eye. It's an anime that will haunt you for years. Even as I'm writing now I'm trying to suppress tears. I watched this anime 6 years ago.
Higurashi no naku koro ni
Nothing about this anime looks particularly interesting or well made. The art and music is alright, the premise is generic and so are the characters. This anime makes up for everything by its mystery and the gruesome consequences it has. The actual mystery is not apparent at first, which is one of the great things about the anime. It will leave you confused for the good first half of the first season until you start to try and figure what is actually going on. My mind was completely blown at the end of the first season. A great example of an anime that is not trying to wow you with visuals or over the top action, but simple and effective narrative.
Claymore
This is actually a cheat in my list. The anime is pretty good but it's a mere entry to get you to read the manga. It's one of the most interesting stories I have ever read and actually the only serious manga I have ever consumed. The art is twisted and beautiful, the story has so many left turns and twists that you will have to throw away all of your expectations. No character is safe in this story and might die on the very next page. Never has a manga, or any book for that matter, made me feel so intrigued, so anxious, so sad, so happy. Before this one I never believed something printed could actually make me cry tears of sadness and tears of happiness and relief.
The anime actually got a butchered ending so they could fit it into a short series, but the manga is just so much longer. So, now go and read the manga!
Toradora
You will find this a lot in recommendations for romance animes but it's just so much more. It's one of the most intelligent animes I have ever seen. The story itself is actually extremely generic and you could see the ending coming from the very first episode. The real meat in this are the characters, which start out as one dimensional tropes and will be fully developed into multidimensional beings that you care and root for. Nobody is really who they seem to be. The conversations between the characters are extremely well written and at times even philosophical. It's witful, funny, sad and overall a very enjoyable ride.
K-On
I know I already named the best comedy anime, so where does K-On fall? Strictly it is just one of those "cute girls doing cute things" animes. But not just one it's THE "cute girls doing cute things" anime. It's not the first but it is without a doubt the best. The girls have depth, their lives and hobbies matter. They are passionate and they have actual problems that pertain to the overall story. Like most KyoAni works the polish is top notch. The eye for detail is astounding. It is a musical anime and music is at the absolute core. You will be able to follow every note on the realistic and correctly animated movements on their instruments. The conversations, the quips are all very well timed and perfectly delivered by the VOs. It's simply a joy to watch.
It's also a precursor to another anime on this list, also made by KyoAni.
Yuuki Yuuna wa Yuusha de aru
Yes, it's one of those animes with deconstructed genres. This one is for the Magical Girls genre. It shows in all its brutal glory the sacrifices real magical girls have to make in life or death battles to save their world. It finds a good balance of comedy and light hearted slice of life to make the heavy drama that follows very effective. The music by Monaca is absolutely amazing and unique and so are the excellent visuals and choreography of the battles in both 2D and 3D. The best Magical Girl anime you will ever watch.
Shirobako
What could be a better anime than an anime about anime? This is probably the most realistic depiction of the world of anime production we have. It is a comedy anime but it does show the struggles of adult employees within the industry. Directors, producers, managers, animators and voice actors. They are all featured, each with their own problems they have to overcome in the harsh anime business. It's a must watch for anyone interested in the anime industry.
Junketsu no Maria
This is not your typical fantasy show. It's the most realistic and mature depiction of the middle ages you've ever seen. It's all about war, morals, politics, religion and sexuality. I have never seen these themes handled in such a down to earth and mature way in any show. And while it does have fantastical elements with Witches and angels it does not feel that way since everything is grounded and restricted by the harsh reality of life in the middle ages. This one just blew me away with its direct approach to every single matter. If you ever thought anime is childish, watch this one. It's not action packed or melodramatic or even necessarily funny. It just hits you with pure unadulterated honesty and the struggle of actual humans with human dreams, human emotions and human carnal desires.
Hibike Euphonium
Oh look, another KyoAni show about girls and music in highschool. This one however has a completely different approach than K-On. It's all about orchestral music, so the cast is much broader. Even more it's about competitive orchestral music, which is the source of the show's drama. It's about the struggle about its mostly female cast to succeed in their tough competition. They have to overcome their own lack of of skill and personal troubles as well as conflicts between the cast.
What makes this anime so great, though, is not necessarily its cast or the story. It's the pure KyoAni trademark polish and detail. This is the prime anime for anyone who likes classical music, as the music is actually the real star of the show. Every single instrument in this big orchestra is depicted realistically to the last detail. To the point where a big part of the best scenes are just lingering shots of said instruments being played. The performances are beautifully animated and directed to draw the focus to the instruments and how they are played and how they create together a full orchestral sound. It all culminates in one of the best final scenes in animation ever and will leave you in awe and make you feel as if you actually just watched a whole real orchestra having the performance of their life.
Haikyuu
The obligatory sports anime. In fact, the best sports anime. A marvel in execution. While it employs the exact same sports anime tropes you all know and love and hate, it does so in an amazingly tightly directed manner so it makes you actually enjoy sport's D-student, Volleyball. It's hard to explain it because on the surface it's really just another sports anime but its execution is just so perfect that you want to watch it, you want to root for the cookie cutter characters even though you can basically predict the outcome of every scene. If you want to try out just one sports anime, try this one.
Made in Abyss
Cutesy anime characters go on a merry adventure and get a brutal reminder of horrific reality in depths where no one can hear them scream. An adventure horror anime with vivid imagery and tragic stories. Beautiful backgrounds, terrific score and movie quality production values make this one of the great anime masterpieces.
Houseki no Kuni
The so far greatest achievement of 3DCG anime. A unique premise matched with the best 3D visuals in any anime ever. Animation and especially the voice work is impeccable and makes this anime a definite milestone and measure for all future 3DCG animes.
I hope this list will help some people who only ever get recommended the same mainstream bullshit over and over.
https://myanimelist.net/animelist/vivster?status=2&order=4&order2=0
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