Contrary to popular belief in the West, shonen is not a genre of anime and manga but rather a demographic. Western anime fans hear the word shonen and tend to automatically think of Dragon Ball Z-style power battles, and its true that fighting anime have an outsize impact in the world of shonen. However, shonen is a word that refers to any anime or manga aimed primarily at teenage boys, regardless of genre. Beyond just action, there are drama, comedy, romance and horror series that are categorized as shonen, some of which you might not have even realized were shonen!
Here are some recommendations for high-quality shonen anime that fall outside of the typical fighting shonen stereotypes. Some of these titles contain action elements, but fighting is not the focus of these series. This list does not include sports anime, an increasingly popular genre of shonen that often plays very similarly to fighting shows but with the fights replaced with sports competitions.
DEATH NOTE
In a way, Death Note could be considered a "battle shonen," but its battles are intellectual rather than physical. The story is an ever shifting-duel of wits between Light Yagami, a sociopath killing criminals using a shinigami's Death Note, and the mysterious detective L (and others later on) who's trying to catch him.
Tetsuro Araki directs the anime with the same over-the-top intensity he'd later bring to more traditional action fare like Attack on Titan. If you're curious how such an edgy nontraditional shonen got made, creators Tsugumi Ohba and Takeshi Obata later made the semi-autobiographical shonen-about-shonen Bakuman.
AZUMANGA DAIOH
People frequently guess the target audience of Azumanga Daioh is one of two demographics. Some see a cutesy, mostly innocent comedy about the ordinary lives of high school girls and assume it's a shojo anime made for high school girls. Others look at how in the years since it's release, this genre has become popular in seinen anime for adult male otaku and assume it's seinen. But they're both wrong -- Azumanga Daioh is officially categorized as shonen. So are Lucky Star and Nichijou, if you're looking for similar shonen comedies.
ANOHANA
Sometimes you just want to watch something that will make you cry. Ano Hi Mita Hana no Namae o Bokutachi wa Mada Shirai (literally translating to "We Still Don't Know the Name of the Flower We Saw That Day" and generally abbreviated to AnoHana) is a shonen anime that will do just that. This heartfelt drama about the ghost of a dead girl reuniting her estranged childhood friends is both amazing and almost sickeningly tear-jerking. Expect Toy Story 3-level waterworks by the final episode.
DETECTIVE CONAN
What's the longest running shonen anime with full half-hour episodes? It's not Naruto or Dragon Ball Z or even One Piece; it's Detective Conan, a mystery series about a high-school detective stuck in the body of a small child. The show never really took off in America, where it was localized as Case Closed. It was simultaneously too gruesome for kids' TV but too cutesy to work on Adult Swim. In Japan, however, Detective Conan is still universally beloved after over 968 episodes.
THE PROMISED NEVERLAND
Later arcs of The Promised Neverland manga become more action-packed, but it never neatly fits into the typical shonen battle formula. The manga's first arc, adapted into the first season of the anime, doesn't fit the formula at all. Without spoiling the details of the story (it's better to just experience it), The Promised Neverland's first season is a psychological fantasy thriller about children working together to plot an escape from a twisted predicament. You have plenty of time to catch up on Season 1 before Season 2 premieres in October.
WELCOME TO THE NHK
It's honestly really weird to think of Welcome to the NHK, a black comedy about social isolation, porn addiction and suicidal depression, as a shonen rather than a seinen. The only logical reason for why this novel-manga-anime franchise was marketed to teenagers is that it could serve as a cautionary tale on how not to live your life as an adult. Older anime fans will definitely laugh and cringe -- and might just find themselves reflecting deeply on their own mistakes and mental health struggles.
THE ANCIENT MAGUS BRIDE
Demographic labels for anime and manga can be extremely loose. The Ancient Magus Bride is a supernatural romance told from the perspective of a teenage girl. There's plenty of magic and a little bit of action, but it's primarily centered around Chise's internal growth and personal relationships. If The Ancient Magus Bride were shojo, it probably wouldn't look much different than it does as shonen. But when girls enjoy shonen and boys enjoy shojo, the distinctions ultimately don't matter, and The Ancient Magus Bride is enjoyable for all genders.
DR. STONE
Dr. Stone has many of the classic themes commonly found in Shonen Jump series: a constant growth of powers, the importance of teamwork, a defiantly optimistic attitude in the face of danger. Where Dr. Stone significantly differs is that it frames these themes not around fighting, but around science. The power-ups aren't mystical but technological; there are sometimes fight scenes, but the main focus is on rebuilding civilization after the apocalypse. The first season of the anime wrapped up last Autumn. Season 2 is expected this Summer, and judging from the manga, this is a series that could last for years without growing tired.
This list only scratches the surface of all the shonen anime, to say nothing of all the shonen manga, that don't fit inside the battle mold. We could have also talked about Toradora!, Durarara!!, Your Lie in April, Monthly Girls Nozaki-kun, and plenty of others. Technically even the infamous Interspecies Reviewers is based on a shonen manga! It all proves that shonen series can be about anything.