Above the Influence: Despite the persistent efforts of The Children (and Kyosuke, and Fujiko, and the entire free world...).
Badass Normal: subverted in the pilot chapter where he's (although completely oblivious of it) a level 7 anti anti ESP-er link... which still makes him a normal guy... but in the serialized manga (and anime) he is just a Normal.
Celibate Hero: Minamoto's life revolves around keeping The Children safe and happy. On the rare occassions when does manage a date he's completely clueless.
Cunning Linguist: English, Russian, German, French, Italian, Chinese; and some proficiency with Spanish and Korean.
Parental Substitute: He is a full time parental figure and role model to at least five very powerful ESPers.
Poor Communication Kills: Chooses not to share the full details of the prophecy where he kills Kaoru. Hard to blame him, but it still leads to lots of misunderstandings and hilarity.
Single Girls Seek Good Man: Minamoto's the first person who has ever shown the Children any genuine respect, love or kindness. They all fall in love with him.
Freudian Excuse: Averted. Despite some horrific treatment at Suma's hands, a prejudice, as well as a childhood of being feared by her family, Kaoru is a kind hearted person. Even as a villain, her stated goal is protecting ESPers rather than hatred of the human race. Still, it's lucky she met Minamoto when she did.
Living MacGuffin: Kaoru's the prize for BABEL and PANDRA. Whether the prophecy is fulfilled is up to her, so both sides work very hard to win her heart and mind.
Blessed with Suck: As a psychometer, she can read people's darkest secrets and feelings, leading her to have a very cynical view of people and also leading many people to being afraid of touching her.
Broken Bird: Shiho mentions in one of her arcs that she learned very early on what kind of a world she lives in. Later, for laughs, she frequently Lampshades that she's a "dark" character.
Mind Over Manners: Averted. Shiho is not above using her powers to jerk Minamoto's chain, or even lie about what she sees in his mind to get him in trouble for the lulz.
Precocious Crush: Like the other girls, she's crushing on Minamoto. She mostly expresses it by messing with his head and getting him in trouble.
Stepford Smiler: Very mildly, all things considered. IF she doesn't want to deal with you, she'll smile, listen politely, and ignore you until you go away.
Taizo Kiritsubo
The leader of BABEL in terms of most day to day matters.
Another ESPer on BABEL's payroll who occasionally assists the children in the field.
Ambiguously Gay: We don't see her in any relationships on-screen, but she isn't interested in Tanizaki (though not many girls would be) and she's the heroine in the Marimite parody episode. Easy to come to conclusions.
Tsundere: Ken calls her one, but she actually doesn't fit the type; she's dere to everyone except Tanizaki, who is not her love interest. And deserves the violence he receives. And likes it, anyway.
Wife Husbandry: Possibly one of the funniest subversions ever.
Yamato Nadeshiko: Tanizaki's pet project is to turn her into one. And mostly succeeds: Naomi is simply a very calm, kind young woman who is far too strong willed to put up with her supervisor's crap.
Ichiro Tanizaki
Naomi's supervisor, and would be suitor
Butt Monkey: He sexually harasses a woman who can juggle trucks with her mind, so he's really got it coming.
The Not-Love Interest: He's placed in the Love Interest slot for Naomi (by his design) and is the most important person in her life, but he is never getting a chance at her.
Wife Husbandry: Unlike Minamoto he is trying to invoke this trope, but it's backfiring badly. And by badly, we mean hilariously.
Bullet
An Esper brainwashed by Black Phantom
Bad Future: It looks like he's in for this. In a recent chapter, Feather shows Minamoto a vision of the future. In said vision, Bullet dies (or at least is critically wounded) after getting in the way of a trap set up for Aoi.
Kawaiiko: She really overdoes the cute sometimes, even though she's a bit too old for it.
Lolicon: She steals The Children's Sacred First Kiss. Generally doesn't have much of an issue with that "age of consent" thing. (Or that consent thing, for that matter.)
A group of rogue Espers dedicated to securing ESPer supremacy, often through violent means.
Kyosuke Hyobu
Abusive Parent: Minor case. His father shouted at him and forced to repress his powers. But it's implied he may have even beaten him for using them.
Adult Child: Kyosuke is defective in basic organizational and living skills.
A Father to His Men: Kyosuke has genuine, no-strings-attached feelings of affection and responsibility for his followers, up to taking over a country just to let the kids go to school.
Anti-Villain: Kaoru sees him as such, though Kyosuke is always zigzagging across the Moral Event Horizon. Regardless, his intentions are at least understandable, and he is providing a home and support network for the espers that BABEL isn't able to find or help.
Brilliant, but Lazy: Kyosuke is as intelligent as Minamoto, but is too whimsical to match him tactically.
But Not Too Foreign: Backstory tells us his mother is 'from the continent' i.e. Asia.
Creepy Child: Had his moments after joining military.
Social Services Does Not Exist: Until Kyosuke reorganized PANDRA, Mio was living in a cabin, on her own, eating virtually nothing but ramen.
Teleporters and Transporters: Her teleportation allows her to teleport only a part instead of the whole like the others. The parts are still connected and if they are too far apart or too far away from Mio, they will reattach on one side.
Hypercompetent Sidekick: Not a match for Kyosuke in power, but he's the one who has to clean up after him and make sure PANDRA is still functioning well enough for him to go off on his larks.
Not so Different: Though it's not explicitly stated, it's clear that he has a lot in common with Minamoto.
Only Sane Employee: You get the feeling that he, Oboro and Minamoto meet for drinks on the weekends.
Punch Clock Villain: Magi treats PANDRA like it's a job: objectives are set, paperwork is organized and you put in overtime to get the big projects done on time. All this makes him more dangerous than the rank and file who treat PANDRA like a hobby or a game.
Ship Tease: With Momiji, who decides very early on that he's marriage material. More so when the only time we see Magi lose his cool is when she gets hurt.
Team Dad: The one who gets stuck trying to establish rules and discipline. Also had to raise at least three ESPers. He's more detached and stern than Minamoto, but given that he works for Kyosuke that's something of a necessity.
The Dog Bites Back: Being always mocked for his hobbies by Sakaki makes it that much easier for him to join PANDRA for good and nearly murdering Sakaki in the process.
In the anime, BABEL really had it coming when Kaoru blackmailed him into building an anatomically-correct Oboro doll for her, then just left him holding the bag when it was discovered, causing him to lose out on his chance to take his girl out.
Freudian Excuse: His coworkers' general disdain for his hobby gives him another reason to spy on them for PANDRA.
Marionette Master: As an esper, Kugutsu can manipulate dolls with life-like accuracy. Also, this.
Otaku: A doll/figurine otaku to boot. Never to be seen without a LiccaMoga-chan doll.
Magic A is Magic A: Momiji's actual power is a synthetic power that allows her to anchor herself in space, effectively giving her super strength.
Ship Tease: With Magi and Kiritsubo of all people.
Shoot the Dog: When she first meets Kaoru, Momiji is willing to engage in unethical behaviour to get her objectives. Then Kaoru tells her that sort of crap won't fly.
No Name Given: He's always referred to as "Black Phantom", "Boss", "Father", etc.
Theodore
Battle Butler: A notable aversion: despite the way he dresses and his loyalty to Black Phantom, he lacks Psychic Powers or other combat abilities.
Phantom Daughter/Yuri Kumoi/Mirage/Phantom
One of The Children's classmates. Actually Black Phantom's daughter, a Hypno user with a split personality. The Yuri personality knows nothing about Black Phantom and has no special abilities; Mirage, who considers herself the main personality, created her to fool Psychometers.
Creepy Child: So brainwashed that she smiles when revealing that Black Phantom has put a device in her forehead that will kill her if Kaoru removes her brainwashing.
A mysterious, very powerful Esper whose mind can be transferred between bodies using raremetal quartz. She has amnesia, but has a vague idea that her goal is to "change the future". In love with Minamoto (even more so than everyone else). Originally implied to be Kaoru from the future, she's actually an amalgamation of the memories of all 3 children (and possibly others as well) from the future, with Kaoru as the nexus.
Grand Theft Me: Does this to Phantom Daughter, although she doesn't really take over, just hide among the other three personalities.
Meaningful Name: She gets turned into a bird for a while. Actually, her name probably refers to Kaoru's angelic wings.