The "protagonist" of the series, an anthropomorphic squid-girl who comes ashore to invade the surface world in retaliation for constant human pollution of the seas, only to end up being forced to work as a waitress at the Lemon Beach House restaurant in order to pay for a damaged wall of the restaurant.
Applied Phlebotinum: In Season 2 episode 2.3 it turns out that Ika Musume can pick up heavy weights with her tentacles because she can manipulate her weight using her bracelets.
Required Secondary Powers: It's eventually explained that the whole reason Squid Girl can pick up people and other heavy objects with her tentacles without losing her balance is that she can alter her weight with her bracelets, becoming heavy enough to anchor herself.
Between My Legs: The shot used when she's introduced. The same introduction shot is used in the first and last episodes of both seasons. She also gets this shot in episodes 3 and 7.
Brilliant, but Lazy: She's shown to be extremely good at math, has mastered several skills that have nothing to do with world domination, and of course there's her extremely powerful tentacles. She could at least be a serious threat, if she wasn't so lazy and easily distracted (and of course, if it weren't for Chizuru.)
Cry Cute: Every time Chizuru intimidates her into obeying her, or whenever a "comrade" of hers (e.g. Takeru in a squid paper-hat and an umbrella) "dies" (Takeru's hat blown away, the umbrella ran over by a truck).
Dark and Troubled Past: Occassionally hinted at. It seems life in the ocean wasn't all that great for her. When Eiko mentions how Ika isn't picky at eating, she responds by saying in the ocean you can't afford to be picky, just being able to eat at all is reason to be happy. She later tells Takeru she had never had the opportunity to play with others until she came to the surface. She seems oddly depressed when these subjects are brought up.
Even the Girls Want Her: Ika is, in an appropriate and friendly way, friends with many kids of either gender, specifically Takeru and Kiyomi's respective groups of friends. Sanae and Cindy, on the other hand...
In season 2 episode 9.1, Ika is asked by Risa to join her play as her husband. Minutes later, Eiko, Sanae, and Kiyomi all join in. They have different roles but they share one similar thing: they LOVE Ika Musume. They even take their roles seriously and act as though they are genuinely in love with her.
Face Your Fears: In Season 2, Episode 11.3, she overcomes her fear of Chizuru, accidentally ticks her off again, and gets dragged by her to a room whileshowing NO signs of fear.
Ika: Oh? About what? (while being dragged by Chizuru to a room)
In fact, this is why she's given the job at the restaurant. Her delicious ink also helps.
Never Bareheaded: And for a very good reason: it's mentioned that her "hat" is actually her life source. If it's removed, she dies. Luckily, removing it is pretty hard since it's fused to her scalp. Since she's a squid, it may actually be her scalp (it certainly looks like the top of a squid's head). She also provides the image for the trope page.
The Generic Guy: Lampshaded when Squid Girl tries to draw the Aizawas using her tentacles (which she explains goes by her mental images of them.) Chizuru gets drawn as an oni, Eiko as a killer robot, and Takeru...is a more photorealistic version of himself.
Made of Iron: His very first appearance has him getting thrown around and slammed into the ground by Squid Girl's tentacles, only to get right back up and proclaim "That was so cool!"
Not so Above It All: Despite treating Ika like a playmate most of the time, Eiko notices that he's slowly learning to subconsciously control Ika — which is easy enough, given her immense gullibility.
Out of Focus: In Season 2 Episode 10.1, Ika, Eiko, and Chizuru all forget about him while they try to eat as many cuts of meat as they can. Luckily, Chizuru has reserved some cuts (which she intends to eat herself) for him.
Love Makes You Crazy: Turned Up to Eleven in Season 1, Episode 10 part 2, when she tries to abstain from contact with Ika Musume. She begins to hallucinate Ika Musume is everywhere and everything; a little girl, a set of trash bags, even as the heads of lanterns.
Beautiful All Along: Without those creepy "Fake Ika Musume" kigurumi masks her father has her wear.
Beware the Nice Ones: After episode 10.2, you better show some manners while talking to her, as her father finds out after she throws him down. Though that one is an accident. She learns self-defense from Chizuru. Yes, thatCHIZURU!
Bodyguard Crush: While very subtle, it's implied that she may be this for Eiko as she tends to be very shy and bashful towards her.
The Faceless: Not exactly with her appearance (she's even actually quite the looker), but she's this personality-wise; as her father told Eiko, she cannot actively interact with people outside her masks.
Meido: In Chapter 162 (Season 2, Episode 2.2 in the anime), she is this while working at the store and while wearing bladed brass knuckles! Needless to say, male customers are petrified at the unusual sight.
Not Good with People: Chapter 210 reveals she can speak normally with Ika, because she doesn't consider her human.
Reed Richards Is Useless: In their zeal to discover Ika's "alien" heritage, they conveniently overlook their other, far more important discoveries: a universal language translator and a cure for cancer. Being that we actually learn this from them, they appear to have some faint awareness of the fact that they're squandering their talents and discoveries
Probably they finance their wild-alien chase with the patent-money they get from these inventions?
Villain Team-Up: While they are not really villainous, the trio and Ayumi's father join forces in Season 2, Episode 11.2 to build a Mecha-Ika Musume. This Mecha-Ika has almost all of the original's powers as well as the ability to speak.