Birds of a Feather: Yukino and Hachiman, no matter how much they deny it. Both are sarcastic bookworms with a matching sense of humor. Both share their cynical view of the world, and, at the same time, feel the obligation to help those they encounter. Both have a truckload of painful social experience.
Two Girls and a Guy: The trope is played in a uncommon way because the guy is the protagonist. On the romance side of things, one girl is interested in the guy. The other girl's interest is somewhere between ambiguous and non-existent depending on who you ask. Although the guy finds both physically attractive, he doesn't want a relationship with either.
We Help the Helpless: Not to the fantastic extent of most examples, but their club mission is to offer a hand to anyone in need.
Hachiman is the story's main protagonist, an isolated, friendless boy who is pragmatic to a fault. His most prominent feature is his set of "dead fish-eyes". He firmly believes that "youth" is simply an illusion created by hypocrites, for hypocrites, born from the ashes of past failures. In this state of apparent corruption, he is coerced into joining the Service Club by his futures advisor in the hopes that exposing him to the world will change his personality, and ultimately make him a "better person".
Ambiguously Bi: Although he does indulge in Eating the Eye Candy when he blunders upon it (while getting knocked flat onto the floor as a female student is passing, for example), he seems more attracted to Totsuka than any of the girls.
Bad Liar: Not always, but when it comes to his romantic history he is. His difference from the usual practitioners is that he mixes lies with facts and tries to reinterpret them in a positive and heroic way. No one is fooled, including himself.
Byronic Hero: Is he intensely introspective? Yes. Is he cynical and jaded and has he experienced a bargain bin of a dark and troubled past bundled with regrets? Yes. Does he see his own values or passions as above everyone else's? Yes. Is he doggedly determined to follow his values and passions despite trampling over others? Yes. Is he especially physically attractive?...No - well, good enough.
Celibate Hero: Actively tries to avoid "Rom-Com" situations, and does not believe that he deserves love. Best shown when he rejects Yui's feelings for him because he believed they were driven by her guilt.
Chronic Hero Syndrome: Despite his outlook on society, if he sees someone in need, he will help them no matter the toll it takes on himself.
Covert Pervert: Never misses the chance to check up on girls (and Totsuka). Every time Yui approaches him, he notices her chest first and everything else later. Manages to appreciate being touched by Hiratsuka-sensei's breasts while she grabs him in Sumo grapple(for your info: hurts like hell). Derives sexual references out of thin air in the first 100 words of the very first chapter... well, you get the picture.
Dismotivation: fits Hachiman to a T. Among the usual reasons, like not wanting to be hurt again, he has an uncommon but somewhat logical argument.
Hachiman: "We only change to avoid the current situation. The true meaning of not running away is planting your feet firmly in the ground and doing the best you can with your present. Who's running away now? Why can't you just accept who you are and were?"
Don't You Dare Pity Me!: He welcomes hatred, rejection, isolation, and disgust. But the one thing he cannot accept is being pitied for what he himself chose to do.
Dude, Where's My Respect?: Members of the Service Club (plus Hayama) know that he willfully provides twisted solutions to club's cases, sometimes taking the heat in the process. Others just see a manipulative asshole.
Heroic Self-Deprecation: A major part of his moral philosophy is that, as long as someone else is happy in the end, it is perfectly okay for himself to be hated or undergo suffering. The implication is that Hachiman thinks of himself as less than others.
Misunderstood Loner with a Heart of Gold: Is definitely a good guy morally, however his methods, as well as his refusal to elaborate to other people his plans, cause his classmates to alienate him further.
My Sister Is Off Limits: Very protective of his sister, and really does not appreciate the fact Kawasaki's brother calls him big brother.
Hachiman (after remembering a rejected confession of the past): "For me these kinds of romantic developments don't happen in real life. In order to prevent a tragedy (read: rejection) from occurring I just have to be hated."
Nice Guy: If you ignore his twisted philosophy, Hikki is actually a really nice guy. He simply has no love for himself and thinks that, by not involving himself in other people's lives, he is doing the nicest thing possible for them.
Not So Different: With Yukino and Hayato, but they also differ in many other ways which leads to the theme of the story.
Opposites Attract: May or may not have this kind of chemistry with Yukino. There is no denying that one of the main plot points of the series is how they interact with one another despite their contrary philosophies; whether or not there is romance involved has yet to be seen.
Though it must be noted that Hachiman admits that he finds her physically attractive, but claims that everything else is rotten.
Perpetual Frowner: His default expression, which isn't too surprisingly considering his outlook on life.
Poisonous Friend: Takes this role much of the time; he may be twisted but he cares enough about others to take the fall for others.
Refused The Call: Hachiman is adverse to joining the service club and leaving his self-imposed solitude. Good or bad, the call can make sure he doesn't graduate in only 3 years.
Rousseau Was Right: Is surprisingly enough a believer in this, as he shows when he quotes Sōseki Natsume
Hachiman (Quoting Natsume): “You seem to be under the impression that there is a special breed of bad humans. There is no such thing as a stereotype bad man in this world. Under normal conditions, everybody is more or less good, or, at least, ordinary. But tempt them, and they may suddenly change. That is what is so frightening about men.”
Selective Obliviousness: Unlike other protagonists in the genre, Hachiman is very observent on the way people act around him. He simply picks and chooses which one he deems are necessary to acknowledge.
Serious Business: When Totsuka offers to trade emails with him, his reaction is a bit overboard.
Ship Tease: Mostly with Yui, and surprisingly enough Saika. At first there doesn't appear to be much with Yukino, but there are a lot of subtle hints as the story progresses. Then there are the moments he shares with Shizuka...
The Snark Knight: Hachiman is both defined by this trope and, in a way, also defies it:
Knight in Sour Armor: While he is antisocial and is pretty much disgusted by all human beings including himself, Hachiman also slips out strangely heroic actions, suggesting a part of him still wants to believe there is good in others, and himself.
Token Evil Teammate: He often fills this role in order to get things done, such as finding and bringing Sagami back when she runs off from the school festival. He does get called out on his seemingly harsh treatment of people when he does this however, even though some of them understand the intentions he has.
What Is This Feeling?: Hachiman has twice, so far, wished to befriend Yukino. There is a good chance he hadn't wanted anyone specific to be his friend for years. However his feelings were promptly crushed - courtesy of Yukino.
Yukino is the leader of the Service Club, of which she is the sole member until Hachiman joins her. She is smart, beautiful, and is nicknamed the "Ice-cold Beauty" for her icy demeanor. She has a twisted sense of "noblesse oblige", and believes that it is the duty of the exceptional (in other words, herself) to help the "lost lambs" of the world. Her personality often leads her to be disgusted at the naivete of others, particularly Yui's, and she does not hesitate to show it.
A-Cup Angst: While she certainly isn't small, she doesn't react well when people compare hers with Yui, Yumiko, Shizuka or her sister Haruno.
Hachiman:"We only change to avoid the current situation. The true meaning of not running away is planting your feet firmly in the ground and doing the best you can with your present. Who's running away now? Why can't you just accept who you are and were?"
Yukino:"If that's so, then there would be no way to relieve concerns and no way to redeem one self would there?"
Borrowed Catch Phrase: Yukino starts using Hachiman's catch phrase "source: me" or it's variants by episode 3.
Broken Pedestal: To Hachiman, who initially admired her for being a strong-willed person and for always telling the truth. This illusion breaks when he realizes that Yukino knew that he was the one her car ran over and pretended to have never met him during their first meeting, and as a result the two grow more distant towards each other.
Brutal Honesty: It's one of her defining personality points, and also the reason Yui likes her so much. Though it is less about a need to be honest and more with the fact that she is a direct person by nature.
Childhood Friend: Of Hayato, or at least their parents know one another and they went to grade school with each other.
Catch Phrase: "I don't lie." Due to this catchphrase, it really hits Hachiman hard when he realizes she has lied to him before.
Chronic Hero Syndrome: Mostly a coincidentally positive consequence of her ambition of Utopia Justifies the Means. Yukino does not actively go out helping people, preferring them to come to her, making this a rather twisted sense of Noblesse Oblige.
Color Motif: Yukino tends to dress in quiet, subdued, black or white colors, which are occasionally accented with the formal purple.
Romantic Runner-Up: Her sister mentioned once that Yukino may be on the losing side of a Love Triangle again between her, Hachiman, and Yui. So Yukino probably did like a guy, who ultimately chose another girl instead. This may partly help explain why she acts like a Jerk Ass towards Hachiman; much in the same way he deliberately wants to be left alone, to avoid the pain of a rejection again.
Utopia Justifies the Means: This trope is downplayed. In her words she wants to change the world in order to avoid the downfalls of human nature. For example the tendency of the talented to suffer for their gifts. Her means of doing that involves bluntly criticizing people.
Will Not Tell a Lie: Is known for telling the truth no matter how harsh it might be, though she is capable of half truths and clever semantics. However, Hachiman finds out Yukino did lie when she claimed she didn't know him before their initial meeting. This puts quite a bit of strain on their relationship.
Yui is a cheerful, outgoing girl who becomes the Service Club's first "customer", asking them to help her bake cookies for "a certain someone". Her problems lie not with her personality, but with her inability to deal with issues by herself. She believes that talent is inborn, and often aspired to be like others until Yukino changed her way of thinking. Following her experience with the Service Club, Yui begins to attend Service Club sessions after school as well, despite Yukino's objections early on.
Ambiguously Bi: When asked by Yukino's big sister what she thinks of Yukino, Yui can't help but talk like a lovestruck highschool girl as she explains. This is while she's already hinted to have romantic feelings for Hachiman. Considering that Hachiman himself is also Ambiguously Bi...
Bokukko: In the anime she's greeted Hachiman with slang usually used by guys and will sometimes speak like one (using "ore" instead of "watashi/atashi") around Yukinon and Hachiman, though she has more of a Plucky Girl persona than that of a traditional Tomboy's.
Cannot Spit It Out: It becomes a little obvious that she begins to like Hachiman, but never states her feelings to him.
Clingy Jealous Girl: While it doesn't show up much, she doesn't seem to like it if another girl expresses interest or even just gets uncomfortably close to Hachiman, such as the girl who wanted help with the athletic festival in episode 13. She also gets a little upset when Hachiman shows a lot of interest in going to a maid cafe in episode 5 with Zaimokuza.
Color Motif: Yui is typically dressed in bright, feminine colors and, notably, her hair is a warm peach.
Cuddle Bug: Yukino is her favorite person to cuddle with.
Hayato is a central figure in class 2F and the ace of the football club. He is extremely kind to other people, including Hachiman, and often offers his help to others. However, he claims that he can never forge a good relationship with Hachiman. He thinks that Yukino is close to Hachiman, and believes that this is due to Hachiman's twisted personality. He seemingly understands Hachiman's acts of social suicide to protect everyone.
Academic Athlete: Turns out he's not only the soccer ace but number two overall in their high school.
Foil: He's Hachiman's perfect opposite; popular, sociable, and nice (though not without his faults). Both ultimately have good intentions, but use different methods. Nevertheless, he has a mostly amicable relationship with him.
Hidden Depths: Initially seems like an overly nice but somewhat oblivious popular guy, but he's far more perceptive of Yukino and Hachiman's methods than most others
Yumiko is a popular girl from class 2F with a pompous personality. She is the main female figure in Hayato's clique. Due to her popularity, she has no trouble making friends and thus has little to no understanding towards people who have social troubles. She brushes off anything she doesn't understand as "making no sense".
Saika is a member of the tennis club who has a feminine appearance, but prefers others to not mistake his gender. He is called "The Prince" by his female classmates. On their first meeting, Saika asks help from Hachiman to join the tennis club, which was brushed off by Yukino. Saika then asked the service club to help him improve his tennis skills. He eventually became one of the few people in class 2F who would talk to Hachiman, and often hangs out with Hachiman.
Ambiguously Gay: The amount of affection he shows to Hachiman may raise a few eyebrows.
Saki is Hachiman's classmate who seems like a delinquent, but wants to make friends deep down. She cares deeply for her brother as she hid her name and age to work in night-shift part-time jobs in order to pay school fees and reduce her family's load.
Big Sister Instinct: Hachiman commented on her rare smile. The cause of her once in Hachiman's lifetime smile was her brother. Plus if Hachiman so much as discomforts her brother, she usually glares at him.
Shizuka is Hachiman's teacher, a language teacher who serves as his futures advisor/counselor. She is aware of Hachiman's supposed "problems", and takes steps to ensure he is freed from them, her first move being to force him into joining the Service Club. However, she appears to have some quirks of her own: she is a young smoker, she is very sensitive about her age, and she is often prone to quoting or copying scenes from popular shounen manga. She also never remembers to knock before entering the Service Club's classroom, much to Yukino's chagrin.
Berserk Button: Mentioning her age or single status will either result in pain (in Hachiman's case) or just make her depressed.
Christmas Cake: It is mentioned that she is somewhere around her thirties, and several characters pray for someone to marry her already.
Corporal Punishment: Shizuka has used it as a threat to keep Hachiman in line. The only times she has actually hit him, however, was simply because he pushed her Berserk Button.
Komachi is Hachiman's younger sister who, different from her brother, is cheerful and lively, and is a member of the student council in her school. She understands that her brother has a corrupted personality but still cares for and relies on him regardless.
Yoshiteru is a student from class 2C who suffers from adolescent delusions. He sees Hachiman as a friend after being paired up with him during physical education lessons. While he is annoying, he has a group of otaku friends he's on good terms with. He aims to be a light novel writer.
Haruno is Yukino's elder sister who is even more outstanding than Yukino. However, unlike Yukino, she shows a good attitude towards other people, even if she has to lie about her true feelings most of the time. While Yukino holds strong animosity towards her, Haruno sees her sister who's constantly trying to overtake her as cute.
The Ace: Intelligent, heir to the family business, a brilliant musician and conductor, extremely beautiful and a social butterfly. The hurdle she leaves for Yukino is very high.