Action Girl: She beats up more people than Booth. She takes on an armored knight (or at least one in a pretty period accurate costume complete with chain mail) with a sword while barehanded and fresh out of a car crash. AND WINS TO THE POINT OF HIM TURNING UP WITH HIS ARM IN A SLING. And appears not to break a sweat. The woman is a stone cold BADASS.
Adorkable: She has her moments of this, particularly in lighthearted moments with Booth.
Agent Scully: No matter how insightful or useful Sweets is, she tends to dismiss his insight. Even treating previous accuracy as "coincidence" because of her dismissal of psychology as a science. She has a similar attitude towards anything even vaguely supernatural.
Friend to All Children: Even though she stated that she would never have children, until she later gave birth to her and Booth's daughter, Christine, Brennan has shown a surprising amount of tenderness towards children, especially ones that are abused. She even came up with a way to entertain babies: "Dancing phalanges!"
Friend to All Living Things: Brennan rarely loses her temper, but she does it every time an animal is hurt or killed out of sheer cruelty. Happens both with an attack dog that was used to kill someone and with a Siberian Tiger shot to cover evidence. Also, occasionally, with pigs.
Hard on Soft Science: A particularly weird example. She's hard on psychology, even though this is generally considered at least as hard a science as anthropology (her own field).
Meaningful Name: "Temperance" means "moderation or self-restraint in action, statement, etc.; self-control."
Even more meaningful is the fact that her name used to be Joy before her criminal parents changed the whole family's names to protect themselves from their former partner in crime; they eventually had to abandon Brennan and her brother to keep said partner from finding and harming their children. Many characters point out that Temperance's need for temperance is a direct result of her parents' abandonment and her subsequent experiences in the foster care system, before which she was much more carefree.
My Beloved Smother: Christine is barely out of the womb and she's already started, getting suspended from the Jeffersonian's daycare for interfering too much.
Mystery Writer Detective: A borderline case as her skills as a forensic anthropologist are far more important to solving crimes than any supposedly ability as a writer.
Especially as she only writes the technical aspects and twisted plotting of her novels. The characterization and steamy sex scenes are due to Angela's input. It takes them a long time to even realize this, as Temperance's writing process was to essentially write Michael Crichton-esque murder mysteries, then loan it to Angela to pre-read, who adds the sex and quips. Once they figure his out, Temperance split the royalties with Angela. Back-dated.
Nerds Are Sexy: It helps that she's played by Emily Deschanel. She has no trouble finding mates. In fact, in the sixth season Valentine's Day episode, she turns down half a dozen hopeful suitors.
Berserk Button: If any one threatens, insults or mildly annoys Brennan, Booth seems ready to do violence.
Also clowns. Even on ice cream trucks.
Also don't even think about hurting his son. While we haven't really seen this in action, he is on record that his protective instinct for Parker outweighs his faith in God himself, which is kinda a big deal.
It can safely be assumed that this now extends to Booth and Bones' daughter Christine.
It's a bad idea to mention that one of Booth's ancestors shot Abraham Lincoln in the back of the head.
Big Brother Instinct: Towards his younger brother Jared, to the point where its somewhat unhealthy for them both.
Cannot Spit It Out: Rather ironic. Booth is the empathetic, emotionally connected member of the duo, able to read feelings and intentions with ease, but he is almost completely incapable of approaching his own emotions/baggage with any sort of directness or honesty. This causes a lot of trouble in his relationship with Bones. It also annoys their friend, colleague, and therapist/shrink, Sweets, who eventually gets fed up with Booth's circuitous and denial-filled approach to getting Sweets's help that he threatens to jump out of a moving car rather than put up with it any longer.
Hidden Depths: In addition to being a jock cop, Booth can lecture and work as a hair dresser and dance instructor. His dad was a barber and his mom a dancer.
Jerk Jock: Booth is a mostly-mellowed version of this trope. While he has outgrown most of the trope's more noxious aspects, he still retains disdain for intellectuals and scientists (although it tends to be more good-natured ribbing with those he gets to know).
The Nicknamer: Calling Brennan "Bones", obviously. He also started calling Dr. Wyatt "Gordon Gordon", due to his habit of introducing himself as "Gordon, Gordon Wyatt". Subverted in that Gordon Wyatt revealed that his first and middle names are both "Gordon".
Obfuscating Stupidity: Most of the cast has realized he's doing it by now, but Gordon is the only one that has straight-out called him on it.
Conspiracy Theorist: Though he refers to any of the associated paranoia as simply having all the facts.
It gets dialed down considerably after Zack is exposed as an accomplice of the Gormogon, whose pathology was partially based on theories about secret societies, though it begins to re-emerge in season 7.
Friendly Rivalry: Although there is initially more than their fair share of animosity between the two, this eventually develops between him and Dr. Goodman. This culminates in "The Woman at the Airport", where Goodman confesses that he admires Hodgins' willingness to stand up to him despite his position of authority.
Friend to Bugs: He's the Bug and Slime Guy. One of his doctorates is in entomology. How much does he love bugs? Enough that at one point he willing hosted a parasitic botfly larva in his neck because he wanted to follow its life-cycle.
Secretly Wealthy: And hates it. Or at least will go to almost any length to keep it a secret, so he can keep his life as just being the "Bug and Slime guy" of the group. Pelant took care of that in Season 8's "The Corpse on the Canopy".
The Smart Guy: Will usually end up doing the most hard science in a case.
Omnidisciplinary Scientist: Which is ironic, because she's the only squint who's not actually a scientist, and appropriate, as she's married to Hodgins, who is both a scientist and omnidisciplinary. That said, she can do almost anything techy or artistic that you ask her to, thanks to the magic of the Angelatron.
Not So Different: More in common with her best friend, Brennan, than might first appear: they both have a rigid code of beliefs and morals, both are incredibly stubborn, and both had a lot of difficulty committing to a long term relationship.
Really Gets Around: To the point that Sweets convinces her that it keeps her from forming stable relationships.
Women Prefer Strong Men: Played with. While she married the 'bugs and slime guy', she expresses admiration on ocassion for Booth. For instance, when he goes into 'alpha-male-get-shit-done' mode, she once exclaimed, "Sometimes he is like....whoa."
Moral Myopia: Fires Wendell when she finds out that he's using medical marijuna to treat his cancer because the Jeffersonian is a federal institution and it's use is illegal; this is especially egregious when you consider the previous antics of the others including Angela being held in contempt of court for being uncooperative during Max's murder trial, Hodgins stealing evidence from the Gravedigger case which resulted in a judge ordering the whole team to stay away from the case, and then the team (including Cam) blatantly ignoring the judge's orders.
The Nicknamer: Hodge-Podge for Hodgins, and Zackaroni for Zack. Oddly, she's one of the only people to call Booth by his first name, Seeley.
And Vino Delectable for Vincent.
Old Shame: Her stint as an actress in a horror film.
Only Sane Employee: By and large, the squints are brilliant, but their eccentricities sometimes gets in the way of them being as effective as they can be. Part of Cam's job is to get corral their conflicting personalities and get them working together as best she can.
The Atoner: As a recovering alcoholic, he has to make amends to the people close to him for all the ways he's wronged them. After his death, the team realizes that if the minor things he feels so guilty for were the worst things he had done, then he was quite a decent guy.
Berserk Button: Try telling him that Jimi Hendrix is a better guitarist than Jimmy Page. I dare you.
That was literally the only time he ever got angry about anything. Ever.
Can Not Tell A Lie: In 'The Babe In The Bar', when he, Sweets, Cam and Brennan lie about knowing that Angela's pregnant, he starts whimpering, covers his face and says "Please, I beg of you, don't look at me directly. Just say what you came to say."
"The Reason You Suck" Speech: After dealing with ignorant probes from the Jeffersonian team about his religion, and a misunderstanding from Cam about something he said, Arastoo finally (deservingly) tears into fellow intern Finn Abernathy while they are investigating the death of a 9/11 victim when Finn asks him if he'd be able to investigate this case due to his religion.
Tsundere: Type B; usually sweet and calm, but quick to anger, as seen in both several scenes where his religion is brought up and the episode in which he introduces Cam to his parents.
Butt Monkey: A mild case, but yes, both Booth and Bones often treat him like this. Booth sees him as little more than a child, whereas Bones vehemently denies the usefulness of psychology and insults him about it.
Sweets: You choked a man until he was unconscious?
Hodgins: A bad man. And you're hinting that if I'd killed him that would make me bad, too?
Dr. Jerk: Originally he was this being less interested in Bones and Booths as his patients and more of case study, to the point that when Booth was order to fake being dead by the FBI as part of an undercover operation, he intentionally ignored his request to tell Bones just so he could she her reaction. But thankfully he got better.
The Shrink: Especially to Booth and Bones, but almost everybody's had a turn with him at one point. It's a Running Gag that people wanting advice pop into his office with no warning. Usually, it's not a problem. Usually. Another Running Gag has a member of the cast questioning his ability to give useful advice... who then follows his advice.
Smart People Play Chess: Was a master in his college years, and a decade later still has the skill to outplay an entire club of chess pros.
Nice Guy: He's firm but gentle when dealing with his patients. He also gets Bones and Booth to be nicer to Sweets.
Old Master: To Sweets. He's older, been a psychologist for much longer, and was able to tear apart Sweet's thesis about Bones and Booth's relationship in less than a minute.
Put on a Bus: Went to work at INTERPOL, before retiring from pyschology to become a professional chef. He made one apperance in Season 5 when Booth sought him for some personal help, and hasn't been seen since.
Shipper on Deck: She's actually the one who gets Booth and Brennan to kiss for the first time, due to her "puckish" side and a strategically-placed sprig of mistletoe. But episode 100 reveals that was actually the second time.
Team Mom: Usually gives at least one member of the team a good talking to in each of her appearances. Bonus points for being the apparently oldest recurring cast member.
Freudian Excuse: His mother, a religious fanatic, washed his hands with ammonia (and made him take baths in it) and taught him that sex was evil. Needless to say, it didn't do his psyche good.
Had to Come to Prison to Be a Crook: He could be a Manipulative Bastard all along, or maybe he learned it while on death row. When we first meet Epps, he's claiming to be innocent and trying to get exonerated, but it ends up he just reveals he's killed even more people than previously thought, so they have to keep him alive while they process the new bodies. When he returns in season 2, Epps is even more manipulative and playing serial killer games, leading the team on a merry chase with body parts as clues.
Monster Misogyny: Literally. Booth even theorizes that Epps hates Brennan because she's a smart, strong, confident woman.
Irony: When Pelant does die, he's overplayed his hand so much that Booth barely seems to care. His death had no effect at all on his killer.
Evil Cannot Comprehend Good: He thinks of everything in purely selfish terms - the concept of people acting against their best interest never occurs to him. This ultimately gets him killed - he takes Brennan hostage and threatens to kill her if Booth doesn't drop his weapon. When Brennan tells Booth to take the shot, even though it could mean her death, Pelant is dumbfounded, leaving him open.
Good Scars, Evil Scars: Booth manages to shoot Pelant in the head early in season 8. Plot Armor saves his life, but the entire right side of his face is a ruin of scars due to the bullet's exit wound.
Eye Scream: His right eye is intact, but the trauma of the bullet passing too close damaged it severely, leaving the organ discolored, bloodshot, and blind.
Two-Faced: The left side of his face is normal, but the right looks like a stitched-together hamburger.
Fatal Flaw: His obsession with Bones is what ultimately leads to his death.
Green-Eyed Monster: Minor example, but upon seeing Bones propose to Booth, he simmers for a good 30 seconds while repeating the recording at least twice, and later orders Booth to cancel the engagement.
Hollywood Hacking: Absurdly proficient at hacking every device imaginable. As of the season 8 finale, he seemingly has the entire electronic infrastructure of DC under his thumb.
In his first appearance, he inscribed a computer virus into bones, infecting the Jeffersonian computers when Angela scanned them.
It's All About Me: A big part of his insanity is a pathological need to be the center of attention.
Invincible Villain: For a long time, until pushing his luck too far and getting a bullet in the throat.
Manipulative Bastard: Managed to trick Booth into getting himself removed from the original case by faking a distress call from Bones, provoking Booth into raiding his house without cause. He was hoping the Squints would also similarly screw themselves over to protect Bones, but that part of the plan failed.
Villain Exit Stage Left: Always has an escape plan when the team manages to get close to cornering him. This is because when he did get cornered, he died.
Would Hurt a Child: As part of a Sadistic Choice, forces Hodgins and Angela to choose between saving Hodgins's fortune as the sole heir to the Cantilever Group and stopping a hijacked predator drone from bombing a girl's school in Afghanistan.