Normal Fish in a Tiny Pond: On Earth, he's perfectly normal. However, due to lower gravity on Mars, he's superhuman by comparison.
Out of Focus: He's the main character of the first three books, then fades into the background for a while so that other characters can take the spotlight, then becomes The Hero again later in the series.
Deuteragonist: In the first book, of which she is the eponymous character.
Distressed Damsel / Defiant Captive: She gets kidnapped a lot. Still, while she doesn't usually fight her captors physically, she's generally quick to show her contempt for them. In Warlord, she once has to be knocked out and carried by her captors, as there was no way they could drag her along with them.
Damsel out of Distress: Sometimes she can get herself out of trouble, or if nothing else, assist John in doing so.
Only Sane Man: By the time of the first book, all Martians are fully aware that the atmosphere will soon be unbreathable. Dejah Thoris is the only political figure interested in any truce to try to prevent this common problem.
Super Strength: Though not to the extent of his dad, he's still stronger and more agile than most Martians.
Ascended Extra: After being a supporting character in Gods and Warlord, she gets to be one of the two central protagonists of the fourth book, which is named for her.
The Beastmaster: she has the ability to command banths, and uses this frequently.
Damsel out of Distress: Somewhat more proactive than Dejah; she shoots and kills a Thern who had abused her and manages to throw off the influence of Tario, who while completely insane was still one of the strongest psychics on the planet.
Grand Theft Me: specializes in this, and has his student, Vad Varo, do it for him.
Grey and Gray Morality: he is one of the few charactes in the books who is not clearly good or bad, but rather somewhere in between. He does do morally quastionable things, yet he also uses his skills as a surgeon to help people.
Mad Scientist: swaps peoples minds for money and later creates an army of synthetic creatures.
Tin Man: Ras Thavas, just like the Toonolians, appears to have reached this state from excessive desire to be The Stoic. He professes to be above such things as sentiment, but when he manifests it, and Ulysses Paxton calls him on it, he is in complete denial.
Psychic Powers: Part of how she maintains the fiction of her divinity; most Martians are mildly telepathic, but the ability is unknown among the First Born- except for her. Carter recognizes what it is almost immediately, though.
Fire-Forged Friends: He and Carter start out enemies, but become allies after being imprisoned in Issus' dungeons together.
My Species Doth Protest Too Much: At first, he's the only sympathetic Black Martian. Note that this is still an improvement on the White Martians, who initially don't have any sympathetic representatives.
A Nazi by Any Other Name: Strange aversion. He's a blue-eyed, blond-haired (well, blond-wigged), white-skinned man who believes himself superior to other races and therefore has the right to exploit them however he sees fit and has a cult of followers who believe the same- but at the time Gods and Warlord were written, nobody had heard of a Nazi. Older Than They Think?
Elite Mook: What he amounts to story-wise, though it doesn't quite do him justice.
Master Swordsman: Considering he's able to overcome the advantage of Carter's super-Martian strength, he's probably the more skilled of the two by a fair margin. Let that sink in. He was almost certainly the best swordsman on Mars.
Worthy Opponent: Carter himself regrets that no one witnessed their duel because of how impressive they both were.