The Ace: Tommy Pickles. Averted in some episodes as he was shown to be the worse cowboy and has a fear of water.
Kimi too. At times, when compared to their toddler personalities, she seems more of an Ace than Tommy.
Suzie's mother Lucy has this carried over from Rugrats where not only is she still a successful doctor, talented artist and chef, she's revealed to have been a successful blues singer at age 18.
All Girls Want Bad Boys: Kimi with Z, and Lil with anyone who shows some rebellion in them. "Chuckie, I've never seen you act like this! ...It's kind of attractive."
Ambiguous Disorder: Dil, who is described as "Not the brightest candle on the menorah", with Phil and Lil mentioning they feel responsible for his mental condition because they dropped him on his head.
Stu: "We're going to get you something every kid dreams of having."
Angelica: "A home in Aspen?"
Dil: "A six week course in Portuguese?"
Chuckie: "Respect?"
Art Evolution: The animation and coloring changes between seasons 1 and 2. Many of the characters were re-designed as a result.
Artistic Age: The kids are middle schoolers but act, are treated like, and even resemble high schoolers. Dil seems like an elementary or early middle schoolers though.
Believes the world is a tetrahedron, dearly hopes to learn to speak with cetaceans, junior UFOlogist, and prefers walking backwards (not just for fun; he thinks it's the clearly superior mode of locomotion).
And it was revealed in an episode that he was literally dropped on his head when he was little. By Phil and Lil.
Though it's left ambiguous whether or not that's the cause. Didi seems to think it just comes from Stu's side of the family.
But it doesn't matter, because his family loves him and appreciates his unique ideas whether it's true or not.
Crouching Moron, Hidden Badass: Chuckie, when it comes to obscure skills and talents necessary to get his friends out of unusual, dire situations. To his dismay, none of these skills would be useful at any other time.
Darker and Edgier: The Christmas episode "The Finster Who Stole Christmas" has a darker tone then the rest of the series, with multiple references to God (even Lil referring to him), sins, and stealing.
The two-parter about the camp with the dissapeared pilgrims' curse.
Dark Is Not Evil: 'Z'. He is a dark, badass, punk, volunteer, helping to raise money for inner city schools.
Executive Meddling and Out Of Order: The season 1 episode "Lucky 13" was held over from airing until August 11, 2004, which marked the 13th anniversary of when Rugrats had premiered. A few season 2 episodes premiered before "Lucky 13".
Friend Versus Lover: One sided Chuckie vs. Olivia for Tommy in "Fear of Falling."
Gang of Hats - Madtooth the Magician's henchmen, who are dressed with a playing card motif. Bonus points for wearing myriad hats with colours corresponding to their suit.
The Christmas episode also refers to God quite a few times. Children's series tend to not talk about religion.
One scene in "A Deville House Divided" has Lil completely stripping a doll naked during a play session with her friend. Luckily, you don't see anything...and then Phil introduces a robot with plungers that fire out of its nipples.
One episode has Didi catching Stu watching a hula girl dancing suggestively on the TV.
Growing Up Sucks: Often averted, ("Fear of Falling") sometimes played with, ("Wouldn't it be Nice?") or played straight, ("Coup DeVille").
Happily Married: Chas and Kira, Stu and Didi, Betty and Howard, and Drew and Charlotte.
Especially Chas and Kira. As seen during the episodes "The Finster Who Stole Christmas" and "Petition This". Sadly, Kira was only in 8 episodes of this series.
Informed Judaism: Averted, as Tommy and his family celebrate Hanukkah, Passover, and Tommy attends classes at a synagogue, and tries to win over girls using the "nice Jewish boy" tactic.
This is carried over from Rugrats, which had Hanukkah and Passover specials.
Karma Houdini: In "Susie Sings the Blues", she pays $1000 to a record dealer to make her a singing sensation. Turns out she was just conned and left out in the middle of the slums. The "producer" disappears from the plot just before the reveal, and recieves absolutely no comeuppance for her actions.
Lad Ette: While Lil does try to be a girly-girl to fit in with everyone else, many episodes show that she's a Ladette at heart. Her friend Wally from the soccer team is one also.
Limited Wardrobe: Played with. Adults have but one outfit each, but the kids have quite a few looks they rotate through.
My Sister Is Off Limits: Chuckie's reaction to Kimi dating. (And to his suspicion that Tommy may have a 'thing' for her.)
Mythology Gag: Many references to Rugrats appear, with the obvious (entire episodes revolving around finding Reptar or Cynthia), to the more subtle (Tommy still keeps a toy screwdriver in his pants, albeit being more sensible to put it on a keychain in his pocket).
Nice Jewish Boy - Invoked by Tommy, who tries to use this trope to impress a girl he likes.
Nobody Can Die - Egregiously, Grandpa Lou, Grandma Lulu, Grandpa Boris and Grandma Minka are still alive.
Noodle Incident: One episode has Lil threatening to blow the whistle on Phil doing "you know what". Subverted at the end of the episode where we find out he spray-painted his skateboard on Betty's wedding dress.
The Other Darrin: Notably averted. Everybody had the same voice actors as they did at the time on Rugrats (Joe Alaskey and Nancy Cartwright had taken over for David Doyle (dead) and Christine Cavanaugh (retired) already).
Overly Narrow Superlative: Chucky is the fastest braces-wearing, red-headed, nearsighted kid on Earth.
Parental Bonus: Betty's hot flashes in "Chuckie's in Love".
Precocious Crush: One of the rare times we really feel sorry for Angelica in "What's Love Got to do With It?"
Put on a Bus: Z. An entire episode is dedicated to him and a possible romance between himself and Kimi in the first season. By the next, all that's left is a passing mention and a brief, non speaking cameo.
Also Nicole Boscarelli, whom Chuckie attempted to impress several times in season one.
Reading Stage Directions Out Loud: Angelica tries to stage Harold desperately asking her to the dance in the hopes of making a boy jealous. It all goes south when Harold dramatically reads out "get down on bended knee!".
She Is Not My Girlfriend: Tommy says this about Kimi when Chuckie accuses him of liking her. (Naturally, it's hinted at the end that he probably does.)
Shout Out: To Rugrats - "The Curse of Reptar". In that episode they're also watching a film that's meant to be a nod to Poltergeist.
"Interview With a Campfire" is a play on Interview with the Vampire. Plus at the start a clip is shown of Lil and Dil re-enacting the opening scene of Scream.
Token Minority: Sad but true, Susie and Kimi, though they are more than that.
Totally Radical: The series made somewhat of an artform of apparently creating pseudo-slang that nobody would ever actually say for no apparent reason. "mondo-weirdo"
Twin Switch: Obviously Phil and Lil in "Runaround Susie."
Two-Teacher School: Played straight sometimes and averted others. Over the course of the series we see about four regular teachers plus their vice principal and some one-off elective teachers... however they also tend to reuse teachers for other classes depending on the episodes. As this is middle school, it's somewhat justified: many middle schools have the students have one main class and a few others, so them having the same teachers all day, with others only being around for electives, makes sense.
Vague Age/Wise Beyond Their Years: from All Grown Up to All Growed Up(Which, while it premiered first, takes place after the series proper): Dil is 9-10, Phil, Lil, Tommy and Kimi are 10-11, Chuckie is 11-12, and Susie and Angelica are 12-13. Each of them tend to act as though they're a few years older.
Vitriolic Best Buds: Susie and Angelica. On the one hand, they're fierce rivals - Angelica is resentful and often antagonistic towards Susie's talent, and Susie shows great disdain for Angelica's meanness - whenever something involves taking Angelica down a peg expect Susie to be on board right away (if not spearheading it) and vice versa. Over the course of the show each enacted some antagonistic plot or another against the other, but on the other hand they're very good friends who tend to look out for each other when the chips are down. In fact, they seem so used to their rivalry that their battles against one another seem like just another part of their friendship.
Walk On The Wild Side Episode: Susie gets told she's too perfect by the popular girls and decides to go bad for the episode.
Chuckie assumes Kimi is going this way in the episode "Bad Kimi". He's wrong.
Wig, Dress, Accent: Lil does this when Phil is pretending to be her (and ruining her reputation). She dons a blonde wig, large sunglasses and sombrero to hide herself.
You Would Make a Great Model: An episode has Suzie meet a woman who offers her a chance to audition to be a singer. The only catch is, she has to pay a fee for a studio session in advance. When she shows up to the "studio" it turns out just to be an office building.
A career aptitude test tells Phil he'd be best suited to being a male model.