In anime, specifically the most popular shonen animes, there is a tendency to focus on the protagonist and his levels of overwhelming power. He (sometimes she) is the one with the strength necessary to defeat the great evil, overcome the great obstacle, and save the day/world/race/universe.
However, it is important that we do not forget those characters who make it possible for these guys to do the amazing things that they do. The characters who sit on the sidelines, but their spirit and mental strength makes it possible for the hero to keep going time and time again.
Krillin - Dragon Ball Series
Despite the hilarity that is Krillin's representation in DBZ Abridged, where he is constantly getting his little bald ass handed to him, Krillin is actually pretty instrumental to the series. He and Goku start out as equals in Dragon Ball, training together under Master Roshi's tutelage, and they remain friends throughout the entire series.
Really, he is Goku's first best friend. Bulma may have come first chronologically, but the age gap, among other things, made it more of a sibling-style relationship. With Krillin, a true friendship was forged.
It is because Frieza kills Krillin that Goku first ascends to the level of Super Saiyan, and it is Krillin who is able to keep Goku grounded in many cases when even Chi-Chi cannot. Were it not for Krillin's friendship, Goku wouldn't be half the Saiyan he is today.
Happy - Fairy Tail
Initially, Happy is a kind of comic relief character in Fairy Tail. The anime is fairly funny in general, keeping things reasonably light in between significantly tense moments. Happy is a big part of that.
Like Krillin for Goku, Happy is Natsu's first true friend. The Exceed has been with Natsu since his childhood, acting as his constant companion for years. He even gets a pivotal role in the Exceed arc, where it is discovered that the world he comes from is devoid of magic. Happy, as his name implies, is a font of happiness for the entire guild.
When his life is in danger, or even percieved danger, it is the spark for Natsu to go basically apeshit all over his enemies, driving him to ever-greater strengths. Metaphorically and literally, Happy is Natsu's wings.
Tsubaki - Soul Eater
Okay, so it's hard to say that Tsubaki is really a "side character" because in truth, she is one of the 7 cores heroes of the anime. Though, the true protagonists are definitely Soul and Maka. So, yeah.
In any case, Tsubaki is the calmest, most well-put together member of the cast, often providing the sound, logical approach to the evils they fight as a team. A direct foil to Black Star's high-energy bravado, Tsubaki grounds him and helps guid him in battle. Their soul resonance is strong, and you could warrant that a lot of that is due to Tsubaki's calmness.
More than any of that, Tsubaki is incredibly powerful, just innately. She is the only current character in the series who has the ability to transform into more than one weapon, including the Uncanny Sword, which is a weapon of nigh-unparalleled power.
Yamamoto - Hitman Reborn
Like with Tsubaki, it's hard to really say that Yamamoto is really a "side" character, because this entire anime/manga is truthfully an ensemble piece. The Vongola family that Tsuna builds has a complex cast of different characters, all of whom have their individual strengths and something to bring to the team.
Honestly, any of them could be on this list. But not all of them have the narrative significance that Yama does. Throughout the majority of the anime, he regards the actions taken by the burgeoning mafia familay as a game, something fun and whimsical that Tsuna roped them into. Even despite that, Yama is a constantly reassuring presence, particularly for their leader, Tsuna.
He is the bearer of the Rain ring, and is characterized thusly as the calm rain that washes away the remnants of the battles. He is that calming force, who keeps Tsuna from being totally overhwhelmed by all of their experiences. This would have you think that he's not the strongest gu yaround, but still, he's a menace with his sword.
Mikasa - Shingeki no Kyojin (Attack on Titan)
This entry virtually writes itself. Mikasa is such a profound badass that her every action reverberates trhoughout all of anime. Where Eren can be inept and doubting of himself, Mikasa is strong and confident. She is uncannily brilliant with the maneuvering system of gas-fired cables, and deadly with her swords.
In fact, Mikasa is the real reason that Eren is still alive. Were it not for her, Eren would have died in the early parts of the anime. She keeps him alive, and she keeps him going when he is down. She is understanding of his rage while in Titan form, and she is forgiving of his actions.
She takes no bullshit and doesn't tolerate disrespect, no matter who is spouting it. she should be the main character of AoT. Yet, as always, women are pushed to the backseat in popular media. Damn shame.