Attractive Bent-Gender: Though it's not really an outright gender bend -Natsume just gets possessed by a Youkai who happens to be female, and who occasionally slips to the surface causing him to to exhibit feminine qualities (sometimes seemingly having longer hair). All of his friends start finding themselves disturbingly attracted to him.
Bystander Syndrome -> Chronic Hero Syndrome: While not being an outright jerk, Natsume had started the series with giving the cold shoulder to youkai who came to him with a problem (which is understandable considering the events that lead to his first meeting of the Fujiwaras). However, as he got a better understanding of youkai, that started to change. Now, Natsume will rush headlong toward Youkai, and all kinds of other danger if he knows someone is in trouble, knowing full well that his opponents are more often than not much much stronger than.
Classical Antihero: Natsume. He's an ordinary human minus the ability to see youkai, and is filled with self-doubt and trust issues.
Consummate Liar: Zig-Zagged. Natsume would usually have to lie in order to cover incidents created by youkai because years Cassandra Truth during his childhood taught him no human would believe him. However, thanks to the help of Fujiwaras and his friends, he has learned to open up to people and has even found others who he can talk about his problems. Because of this, in more recent chapters, people who are close to him can now tell if he is lying or hiding the truth (secretkeeper or not) though they don't always choose to voice it. For the most part
Cuteness Proximity: A mild example, but Nyanko-sensei calls him out on it once, saying he's far too nice to youkai he thought were cute.
Death Glare: Parodied: Natsume's sometimes give this look with often Nishimura and Kitamoto unintentionally at the receiving end, usually after dealing with youkai (though played straight in chapter 26 when he initially suspects they are possessed). However, in more recent chapters, they now assume he just not feeling well.
Did You Just Punch Out Cthulhu?: He frequently knocks out strong youkai with a punch, the most frequent victim being Madara. It's useless against humans though, since it's his Soul Power which does all the work, rather than his physical strength.
Distressed Dude: Natsume has the bad habit of getting captured frequently. For instance, in episode 5 of season three, he gets captured by an ayakashi that's intent on cutting off his arm so that it can use it to retrieve its lost head. Natsume's friends are left frantically searching the house for him. He's also been kidnapped by Matoba two or three times. Nyanko-sensei usually bails him out when he doesn't get out himself.
Identical Grandson: Natsume Takashi looks a lot like his grandmother Reiko, original owner of the Book of Friends. and since many (if not all, Hinoe certainly seems to express a preference) Youkai don't really care too much about gender, Natsume tends to get Youkai who are looking for his grandmother on his tail.
Taken to it's logical conclusion when someone calls Natsume "Girly Man".
Not Good with People: While his ability made it hard to talk to people in general, this seems especially with children.
Orphan's Ordeal: A good bit of Natsume's difficulty with people (and his reluctance to tell the Fujiwaras about his abilities) stems from the fact that, up until then, he was passed around from relative to relative because nobody wanted to deal with the Creepy Child that kept telling "lies" about seeing ghosts and Youkai.
Abusive Parents: Chapter 31 confirms that several of the parents he's lived with were physically or emotionally abusive.
Parental Neglect: Also confirmed in the aforementioned chapter that some of Natsume's parents also forgot to feed him as well.
Parental Abandonment: Natsume's parents are dead, and every single family he's lived with before the Fujiwara's looked forward to the day he left their family, since he could see spirits.
Silent Scapegoat: Natsume often wound up as one in his adolescence, when Ayakashi started causing acts of vandalism around him; his options were either to let everyone believe he was some sort of delinquent, or let them believe he was some sort of crazy delinquent.
Amplified Animal Aptitude: Downplayed but Nyanko-sensei seems to be really good with his fingers/paws in cat form. For example, he can hold chopsticks, hold teacups, reading the economic section of the newspaper, etc (though he still relies on Natsume for opening cans and such).
Jerk with a Heart of Gold: For all his claims to be a ruthless, cruel and uncaring monster who threatens to eat other youkai or humans on a whim, Madara is terribly benign compared to many other youkai that appears in the series. That image stayed for a little while to begin with, but is completely shattered when Madara pulls a Ghibli-style rescue on a little girl who fell down a cliff. Wanting the Yuujinchou was definitely one of his most important motives, and even this is called into question when Madara tempted Nastume to drink mermaid blood. Nastume called him out on this, saying if he was immortal, Madara would never get the Yuujinchou, to which Madara lapses into silence.
Just Eat Him: What he has considered to do to Natsume if the Book of Friends gets any smaller, and tried often, but failed. He even unintentionally tries to "sleep eat" Natsume on occasion, which yields similar results.
He often forgets the deal he made with Natsume, embellishing it with many small details, such as saying that he's being given permission to eat Takashi when he dies to other rival youkai.
Noble Demon: Madara continues to insist that he's really nasty and uncaring and only hangs around Natsume because the latter is his prey (or alternatively his servant). He's not really fooling anyone.
Not so Above It All: Nyanko-sensei regularly brings up his truly awesome powers and the fact that he is "not a fortune cat, damn it!" - until Natsume starts petting him, or hangs a toy in front of his face. Or he spots a grasshopper. Or a little girl has fallen down a cliff and needs rescuing.
Not Your Problem: Tries to convince Takashi into this, but, well, doesn't always work.
Papa Wolf: Don't harm Natsume if you know what's good for you.
Good Parents: She shows genuine concern for Natsume despite not being intermediate family. She first visits him and offer him to live them despite the rumors about his reputation. She also scolded Natsume when he suddenly left the house for a day without giving her a proper notice.
Muggle Foster Parents: He is unaware about Natsume's ability though it is possible that he might suspect something. His kindness has help soften Natsume's outlook on life.
Open Minded Parent: One chapter has Natsume completely wreck a room due to an exorcism spell in order to get rid of youkai that cursed the house. When Shigeru stumbled upon this room, looking like a very familiar incident of the past, he let's it slide as he knew Natsume did not purposely try to wreck the house. In later scenes, we do see him being more supportive of Natsume and him being against putting too many limitations on Natsume's freedom.
Missing Mom: While his mom didn't appear in Kitamoto's special focus chapters, it is mentioned that she is out working since their father is ill.
Nice Guy: One of Natsume's first friends after moving with the Fujiwaras. Warns him about the violent senpai and tries to protect Natsume twice from some unseen youkai during his special bonus chapters.
Those Two Guys: Along with Nishimura, though contrary to the trope, they have fairly important roles in the plot as one of the few (non-psychic) people who are close friends of Natsume. They also get more screentime than anyone other than Natsume and Nyanko-sensei and a fair bit of fleshing out in the manga.
Chivalrous Pervert: In most series, he would not be considered this. In such a series as this, when he is the only one of Natsume's companions who has a crush on somebody and insists that they should have a cafe with bunny girls for the school festival, he comes off as one.
Innocently Insensitive: One of the author's notes in volume 13 states that he gets into conflicts due to this.
The McCoy: Allegedly the most soft-hearted of Natsume's friends.
Sibling Ying-Yang: Nishimura is more laidback and cheerful while his older brother is more studious and stoic.
The Unfavourite: His family is mainly preoccupied with his older brother's studies, going to the point where Nishimura makes his lunches himself.
Action Survivor: Deconstructed in the Omibashira arc when Tanuma is forced to become this after Natsume is kidnapped to become a meal offering. Despite the strain from being near youkai, he does manage to disguise himself as a one and sneak into the place. He tries to free the real Natsume by making a bluff but almost gets caught and attacked. Things begin to go downhill from there
The Quiet One: At first, but that was only because an evil youkai cursed her, so that the last thirteen people whose names she says will die. Natsume helps her break it. After that, she became more like the Genki Girl.
Parental Abandonment: Downplayed but most of her family is out of the house: both her brother and father are overseas while her mom often comes late back from work, making Taki feel most closest to her grandfather who is dead.
Secret Keeper: Asked Natsume's help after hearing about his ability from a youkai. Along with Tanuma, she helps Nastume give distractions to his other friends.
The Smart Girl: Knows quite a bit of youkai folklore and its relations to the surrounding area, thanks to her grandfather's books.
Unfazed Everyman: One of Natsume's friends who know his secret but doesn't have the ability. She still is quite knowledgeable about them and has encounters by herself, thanks material grandfather left behind. Chapter 64-65 actually explores on the idea if ordinary humans should have contact with the supernatural.
Adaptational Villainy: Downplayed. While he is still a "villain" in both the anime and manga, there are some differences. For example, he pulls out a knife and attempts to stab Nyanko-sensei whereas he never does this in the manga. Also, he tortures a youkai just because it entered a human home while he does in the manga to also get information from Natsume.
Blood Knight/ Spirited Competitor : Bordering between the two, seems to enjoy the challenge of a tough youkai, sounding especially disappointed when Madara wasn't going to fight back after pressing his berserk button.
Enemy to All Youkai / Youkai Hate Him: His clan is notorious for their exorcise methods and contracts. Matoba himself makes it clear of his disdain for them. Youkai aren't particularly fond of him either except for some of his servants
Not much nicer to humans either. Was initially going to leave the rampaging youkai to harm the nearby town, along with the unconscious exorcist to die. Later on when he "invites" Natsume for tea, he tells how wonderful the Fujiwaras were "for taking care of a seed so rotten that harmed other children".
Manipulative Bastard: He manipulates Natsume into helping the Matoba Clan expose an exorcist possessed by a spirit that hates the Matoba Clan and attacking them by conveniently leaving out exactly who was being attacked. See also Blackmail above.
Jerkass: Like Matoba, she uses youkai as bait to draw in powerful shiki and sees nothing wrong with it. The anime's back-story reveals that she does not mind exorcising youkai as she is taught it is the way to keep the world in balance.
Precocious Crush: Maybe, but he probably just really, really, really admires and looks up to Natsume as a Big Brother Mentor. The rock God's "humans, ayakashi, and beasts have different times" speech to the fox child in season three about why he and Natsume shouldn't be together and his resulting angst seemed to imply something else though.