Princess Tutu. It's a fantastic amalgamation of various fairytales with a heart all its own that really makes you care in ways you wouldn't expect from the start. Mobile Suit Gundam, Stardust Memory, and Zeta Gundam also comprise an absolutely fantastic story too. Just don't watch past Zeta.
Since this is story wise and most of my favorite anime aren’t story based, there’s not for me to choose from xD However I do have one story based anime in my top 10: Steins;Gate. It’s a great show, definitely worth it. Other than that Inuyashiki and Little Busters! have a great story too.
I'm kinda everywhere with anime, I usually like it if I like the characters, regardless of plot. So that would include anime such as Haikyuu!! and Made In Abyss, both of which I highly recommend (and are on two totally different sides of the spectrum).
It's hard to make a recommendation when I don't know what you've seen and what you haven't. Made in Abyss is one of my current favorites. Without giving too many spoilers, I like stories that feature children in tough situations (since to them the scale of difficulty is much greater from the start anyway) and MiA definitely delivers.
https://myanimelist.net/anime/23273/Shigatsu_wa_Kimi_no_Uso Your Lie in April is one of the most beautiful series I've ever seen. I couldn't control my sobbing by the end, but every minute was worth it. Really interesting characters and a relationship that develops so powerfully and beautifully. I really recommend this series. =) For action, 100000% recommend Hunter x Hunter (2011) and Fullmetal Alchemist: Brotherhood. The former has some minor pacing issues in the later arc but is still very unique and extremely well crafted, while FMA Brotherhood is a masterpiece in its own right. No anime fan should miss out on these two.
I agree with Awney. I really need to rewatch Soul Eater, it's been years since I've seen it. Also, if you like things that are a little on the spooky side, Ghost Hunt is one of my favorites. I don't hear it mentioned very often, so it might be a little on the obscure side.
Well, I don't really have a favorite, but I can give you some recomendations. One anime I really enjoyed was 'Erased' (or 'boku dake ga inai machi'). I won't give you spoilers or anything but I really enjoyed it. If you're looking for something more lengthy, than I recomend 'Soul eater'. It's longer than erased and has more jokes.
Fullmetal Alchemist: Brotherhood is amazing, though I also enjoy Puella Magi Madoka Magica, if you want a short but good anime with no filler.
My all time fav anime is Kamisama Kiss. It has a unique and fun story of a high school girl, Nanami, who lost her house because of her father's debt and suddenly is greeted by a man who claims that he is a Land God. He passes some of his powers to Nanami and she begins her life as a Land God living in a shrine and eventually falls in love with a half human and half fox, Tomoe. They look super cute together, by the way. Spoiler: Kamisama Kiss. You should watch it. Its super fun.
While One Piece is my all-time favorite anime, I can't say it's my favorite from a story standpoint. No, for that, I'd have to go with shows like Steins Gate, Made in Abyss and I might even go with Spice and Wolf even if the character interactions are more where the real draw of that show comes from.