If there's one thing shonen anime is known for, it's having the protagonist(s) and deuteragonist(s) matter to the story being told. There are a number of famous and infamous examples of such anime and characters.
Above all, all of these deuteragonists in shonen anime share common traits and tropes attached to them that ultimately make them important or otherwise link them. It's just as well, considering how popular shonen anime is, that today we indulge in uncovering some of them.
Note: Spoilers will abound for most of the popular shonen anime. This article is likewise only the author's opinion.
Loners, and 9 other very common shonen anime deuteragonist traits and tropes
1) Protagonist friendship/obsession
Most shonen anime deuteragonists have some kind of relationship with the main protagonist. Sometimes it's a huge and long-spanning rivalry like the one between Dragon Ball Z's Goku and Vegeta. Similarly, other times, it's a lasting friendship like the one between Yu-Gi-Oh!'s Joey Wheeler and Yugi Moto. Whatever the case, usually the deuteragonist will have something to do with the lead.
This can result in many possibilities, sometimes a rivalry can bloom into a friendship if not love. Other times, good friendships die or sour and become bitter rivals if not complete enemies like the friendship between Eren, Armin, and Mikasa in Attack on Titan.
2) Opposite personality to the lead
If a shonen anime lead protagonist is a confident, joyous person, then chances are the deuteragonist is going to be a sour, cynical person. Kaiba and Yugi from Yu-Gi-Oh share this dynamic. Likewise, so do Vegeta and Goku and more explicitly as rivals, with Vegeta being full of pride and angry, in comparison with Goku's more lax persona.
It doesn't need to be rivals, however. In the shonen anime The Melancholy of Haruhi Suzumiya, the entire SOS Brigade all have something crazy about them besides the "normal" protagonist Kyon. This usually leads to fun antics and a dynamic between the protagonist and the deuteragonist that usually lasts for the entire show.
3) Family trouble
This one isn't a recent trait or trope by any means, but a lot of deuteragonists usually have family troubles of some kind.
This can manifest itself in families torn apart like the Uchiha in Naruto, controlling families like Killua Zoldyck's in Hunter X Hunter. It can even be divorces that lead to bad situations down the road like Joey Wheeler from Yu-Gi-Oh or abusive families like Crona's from Soul Eater. It's rare for a shonen anime deuteragonist to have a happy family situation.
This is, again, a foil to the protagonist. The protagonist usually has a great family, or people in their lives that make them better. As family situations affect kids and adults later in life, it's not uncommon to see deuteragonists used as a lesson in how bad family trouble affects people.
4) Aspirations of glory
Quests for glory, gold, or fame aren't necessarily bad qualities. A person can go on a quest to become famous, or for the experience and not be shallow or arrogant about it.
Many deuteragonists share the protagonist's dream of glory, but for different reasons. Some do it for themselves, some for family, and others just because they want to be the very best.
Many deuteragonists find themselves in pursuit of some glory - the Number 1 Hero spot, Pokemon master, World Champion, Wizard King, Hokage, the list goes on. The way it gets into villain behavior is when it's sought using selfish means like cheating or back stabbing.
5) Redemption arc
If the deuteragonist goes evil, is evil, or is just a huge jerk in a shonen anime, fans usually expect some kind of redemption arc to happen. From Vegeta to Kaiba to Sasuke, there are plenty of examples of where this ends up happening.
Even so, this isn't a bad trait or trope in the slightest. Sometimes it leads to epic moments like when Vegeta punched Beerus for hitting his wife Bulma.
There are plenty of arguments going on about whether these redemptions are deserved or not, and fans are usually split between acceptance and rejection. Like everything else, it depends on the execution. Not every rival needs to learn to be better just as not every deuteragonist in a shonen is going to be a good person or a loner.
6) Being a loner
Shonen anime deuteragonists are usually loners by choice, choosing to try to get where they want by themselves. This often doesn't work out for them because they don't think things through or believe they alone can handle whatever's coming in life or at them. Sometimes they're right, sometimes they're wrong. Seto Kaiba is definitely the latter, wrong about doing things alone.
Either way, if there's a deuteragonist in a shonen anime, they usually tend to prefer being alone and see others as burdens on them. This is notably changing, or at least has the opposite effect sometimes, like Joey Wheeler or Koichi Hirose being good friends with the protagonists of their shows.
7) Thematic opposites
If there's a light motif to the protagonist, the deuteragonist is the darkness. If one is the hero, the other is either a villain or anti-hero. This is shown all over the place, from Naruto to Dragon Ball Z to Death Note, where heroes and villains exist and the protagonist and deuteragonist are on opposite sides of the spectrum.
Sometimes, like the Death Note, the lines are blurred but the opposites are there. It just depends on the context and what the deuteragonist is in opposition to and what the protagonist is in opposition to. Eren and Armin in Attack on Titan, for example, go in completely different directions, but were always opposites even when on the same side.
8) Anger issues
Some deuteragonists in shonen anime are the off-the-wall type, while others have anger issues that could fill a book. In the case of these deuteragonists in shonen anime, it's more common for them to have hair trigger tempers that go off at the slightest offense or at least have them get mad at the weirdest things.
Vegeta hates losing to Goku and will often express this displeasure in angry barbs. Bakugo is the crowning example as he will literally blow his top thanks to his powers revolving around explosions. It's usually the case that a typical shonen anime rival will have this flare up.
9) Trauma
Overlapping with being opposites, trauma usually follows a lot of deuteragonists in shonen anime. They're usually holding back some key details about their past or themselves that made them who they are. This is usually some kind of traumatic event that hits them at a critical time in their childhood or what they went through that's often untreated.
Sasuke has untreated trauma from the Uchiha Clan Massacre in Naruto. Meanwhile, Levi Ackerman in Attack on Titan had a horrid upbringing and then saw his squad die in front of him and Vegeta had the genocide of the Saiyans. This list of trauma suffered by the characters and how they got through it goes on in practically every shonen anime.
10) Importance
Above all, one thing that unites deuteragonists in shonen anime is importance. These characters are often very important to whatever the plot or ongoing story of their respective series is.
Vegeta is important to Dragon Ball Z for more than just being Goku's rival, he's one of the last Saiyans and his actions have major repercussions in several arcs. Sasuke is another great example of this, particularly when he strikes out on his own and his actions begin to disrupt the ninja world.
Of course, this applies even in anime where the stakes aren't quite so world-shaking. An example of this would be the investigation into Yoshikage Kira in JoJo's Bizarre Adventure Diamond is Unbreakable. Here Koichi Hirose ends up doing a lot of the detective legwork with Jotaro.