Badass Bookworm: His badassery is in his cleverness, because he's all but useless in a fight. But yes, this is a wily con artist who dreams of going to college and whose early forays into forgery included faking a bus pass when he was little so he could get to school on time, because he loved school.
Born Lucky: Peter feels Neal was this. Neal's back-story suggests otherwise (maybe). There's merit to Peter's view.
Neal's not really all that lucky. Until the age of 18 he had absolutely no idea who he really was or who his father really was. That and while he does have his lucky moments, you take into account that the few people he gets close to end up getting into deadly situations even when it's not his fault, as proved with Ellen.
Con Men Hate Guns: Just because he hates them, doesn't mean he doesn't know how to use them.
Daddy Issues: All of them. Like...ALL of them. Pick a subtrope. Father/surrogate conflict, abandonment, idolization, broken idolization, fears that he turned out like him, ALL OF THEM.
Some Mommy Issues on top of that, too, because, according to implication, she was nursing a psychological trauma and/or substance addiction and wasn't really on top of it. He doesn't like to talk about it, even to Mozzie.
Non-Action Guy: He doesn't know how to fight. He admits he doesn't know how to fight. Sometimes, if you have hurt one of his loved ones, he will lash out, but he usually very quickly loses the upper hand.
Not So Different: Neal and some of the criminals he helps put away. Particularly Keller.
Peter is an FBI agent in the white collar crimes unit. He's a straight arrow, and he's dedicated to his profession. He's as good at his job as Neal. He's dedicated to his wife, like many cops, but he actually manages to make it up to her when the job gets in the way.
Adorkable: Peter plays video games (well, Angry Birds at least) and fist bumps (with explosion) with Elizabeth. And you should see him flirt. Well, try to flirt.
Always Gets His Man: Peter's the only law-man to catch Neal. Twice. (it's really more like 2.5)
Berserk Button: Peter loves his wife very much. DO NOT mess with Elizabeth or try to bust up her shop, even if you are an FBI agent. He will punch you in the face. And that's just for starters.
Catch Phrase: "Damn it, Neal!" whenever Neal does something he shouldn't. So all the time.
Expansion Pack Past: Every once in a while, we hear about past career options that were taken away from him or that he chose not to take, among them accountancy (for which see below) and Major League pitcher (for the latter, he actually played AAA minor-league ball until injuries kept it away from him).
Hidden Depths: Peter is shown to have proficiency in a number of fields that even surprises Neal, such as being an experienced horse rider, knowing how to speak Chinese, skilled enough at baseball to have been a potential major leaguer, and possessing a very prestigious accounting degree.
Tranquil Fury: When he realizes that Fowler and his men have been in his house, he very calmly works out what they've done. His voice doesn't raise up, and the only vocal indicator that he's upset is that he's speaking faster than normal. But his face has pure murder written all over it.
"Or maybe you've been chasing him so long you don't know how to stop?"
Elizabeth is Peter's wife. Like the typical "cop's wife", she has to suffer her husband's dedication to his job: frequent absences and missing important occasions. Unlike the typical cop wife, she puts up with this with good grace.
Action Girl: Elizabeth gets her moments. For starters, she once threw a chair through shatterproof glass.
Always Save the Girl: Since she's the only one who isn't a trained cop or a professional crook, she's seen as the one usually most in need of protection, which means that on the few occasions she's pulled into the conflict, everything stops to help her.
Badass Damsel: As of the season three mid-season premiere. She concocts a brilliant escape plan with nothing but a dog bite, thermostat, diamond ring, and some crazy chair swinging skills.
No Sympathy: Averted with Elizabeth, who never seems to mind (too much) when Peter's work gets in the way of their personal life. When a fugitive FBI agent inadvertently hijacks Peter and Elizabeth's date night, she acts more like he's stuck in traffic than anything. To be fair, she asks Mozzie for Peter's safe word to make sure he's okay first.
Took a Level in Badass: When kidnapped, she rescues herself. Not by resorting to typical seduction tricks, but by manipulating her guard (by telling him he'll start sweating if the dog bite he got was infected, then turning up the heat.) While he was out looking for bandages, she then figures out a way to throw a chair through shatterproof glass.
Understanding Wife: She, resignedly, accepts the problems of Peter's job. And Neal's lifestyle. And Mozzie's quirks. She's the living god of, "You're just plain okay."
Mozzie (Willie Garson)
"It's about doing what we want to do. Who cares about nine-to-five's and 401-Ks. Playing by the rules only makes... borders. They just... take away everything that's good about living life."
Mozzie has a criminal mind, but not a criminal soul. You can trust him with your life, but you'd be daft to trust him with a dollar. (Thank you, Sir Pterry.)
Bad Bad Acting: Averted, he is the worst "actor" in the main cast, yet tends to be only a little hammy.
Berserk Button: Mozzie gets riled up in "In the Red" when he finds out that the perp Neal and Peter are going after is running an extortion scam involving adopted kids. This is because Mozzie was raised under foster care and understands the hardships adopted children must go through.
Crouching Moron, Hidden Badass: Mozzie is in no way a moron, but he's generally not a physical presence. Then, in a tense moment he disarms a bad guy and holds him at gun point without flinching. That he nearly collapses afterward just shows how cool he was during the moment.
He knows his appearance gives people a certain impression and uses that to get them to underestimate how quickly and creatively he thinks.
Butch Lesbian/Lipstick Lesbian: A blend between some of the less stereotypical qualities of both (dresses nicely, slams big guy's heads against cars). Her sexuality is never, ever, played for titillation or laughs, and it doesn't define her personality.
Cuteness Proximity: Went to South America to investigate the smuggling of Nazi loot. Came back with pictures of the local llamas.
Cynicism Catalyst: Missing, possibly dead, big sister. She's referenced her lack of closure and abandonment issues stemming from it. It could also explain her dogged obsession with finding stuff at any cost.
I Did What I Had to Do: This is how she operates as a rule, both in her job and otherwise. An example would be aiding in the theft of an item she was insuring to prevent the robbers from killing anyone in an attempt to get it.
Hidden Depths: June shows herself to be an excellent actress during Neal's commutation hearing.
Like a Son to Me: June says these exact words about Neal during his commutation hearing, complete with tears. It's not clear whether she truly meant it though, since she was putting on her best act to help Neal go free. It's probably true to some extent.