Chinpui

Yet another of Fujiko Fujio's innumerable Manga co-productions, Chinpui is basically Doraemon for girls. Most of the former's cast are replicated in some form or another, right down to a lumbering Gian lookalike. The main difference is that the "hero" is a girl and the Magical Helper is an extraterrestrial mouse (as opposed to a robotic cat).

Eri Kasuga is a high-spirited Japanese Tomboy who - for totally inexplicable reasons - has been chosen to marry Prince Lulealv of the Planet Mal. In light of this momentous occasion, two envoys have been sent to Earth to announce the upcoming betrothal: Chinpui, an oversized, wish-granting mouse; and Wandayuu, a lethally annoying talking dachshund. Like most of Mal's anthropomorphic population, they can perform miracles by simply shouting their names (with the usual disastrous results).

Needless to say, Eri is none too thrilled with the prospect of marrying an alien she's never even met, particularly since she's only eleven years old (in addition, she already has a "sort of boyfriend"; Uchiki-chan, the quiet smart kid who lives down the road).

Faced with this overt rejection, Wandayuu departs to discuss the situation with the Royal family, leaving Chinpui behind to serve and protect "their future princess." While Eri initially regards Chinpui as a nuisance, he soon proves himself a loyal and trustworthy friend, especially when it comes to solving the inevitable problems caused by Wandayuu's meddling schemes. Hilarity naturally ensues, as Eri is besieged by spacefaring freeloaders, bickering aliens, unexpected nudity, and at least one superhuman rival bent on eliminating the competition.

Tropes used in Chinpui include:

Action Girl: Eri powers up on several occasions, usually with ~~unexpected~~ ~~catastrophic~~ the usual consequences.
Animated Adaptation: 112 episodes broadcast between 1989 and 1991, along with a 40 minute animated movie (Chinpui: Eri-sama Katsudō Daishashin, aired in 1990). Both were surprisingly faithful to the original manga.
Bad Future: Inverted to some degree when a time traveling visitor informs Eri that she's destined to marry Lulealv within three years. Despite her initial misgivings, it appears that she will actually fall in love with the Prince at some point.
- Almost inevitably, the time traveler turns out to be her own son, who wanted to meet his mother when she was his age.
- The family resemblance suggests that Lulealv is not only human, but drop-dead gorgeous to the bargain.
Barbie Doll Anatomy: Averted in the manga, especially when Eri receives a life-sized anatomically correct "boyfriend doll" from Prince Lulealv (which she promptly returns). The anime version wasn't quite as explicit (though it was pretty damned close all the same).
Be Careful What You Wish For Wish Fulfillment. See last three examples for details.
The Bully: Ooeyama, the series' resident Gian clone. Trope somewhat averted when he gets beaten up by various aliens, the most famous being a badass talking anteater with the coolest shades in the cosmos.
Butt Monkey: Eri's long-suffering Father, for some unknown reason.
Cool Shades: Majiro, the talking anteater referenced above. Beats the living crap out of Ooeyama after he teases Eri in the street.
Cowardly Lion: Uchiki-chan. Despite his diminutive stature, Uchiki constantly stands up for smaller children being bullied by Ooeyama, (and frequently takes a beating for his trouble).
The Faceless: Prince Lulealv. Although never actually seen in person, Eri often dreams that he literally has no face.
Hammerspace: Chinpui stores an infinite number of reality-warping devices in his ears (Yes, that's right - in his ears). This being a Fujio series, most of his gadgets cause more trouble than they're worth.
The Rival: Darusa, a superpowered contender for the throne. Comes to Earth several times, planning to remove Eri from the equation, only to discover that Chinpui has a Badass streak of his own.
Robot Buddy: Chinpui. OK, while he's not technically a robot, he occupies precisely the same role as Doraemon, right down to Time Traveling excursions to the Jurassic era.
Rube Goldberg Device: Many of Wandayuu's grandiose schemes involve ridiculously complicated doo-hickies, all of which backfire on the usual suspects.
Spoiled Brat: Eri's neighbor, Sunemi. An insufferable blowhard, she spends most of her time bragging about her family's wealth. Frequently upstaged by Eri's down-to-earth modesty.
Tomboy: Eri-chan, without a doubt. In Japanese culture, jumping fences and storming in through the back door is considered extremely unnatural for girls of any age.

Running Gags:

Chinpui's humor follows much the same pattern as most other Fujiko offerings. Running gags involve slapstick and domestic comedy, particularly the chaos wrought by Wadayuu's unwelcome visitations:

An exuberant tomboy, Eri constantly tries jumping the fence on her way home, often landing flat on her face with her skirt over her head.
Eri's mother's despairs that she'll ever find a husband, as she avoids housework like the plague and can't cook anything apart from ramen.
- Fortunately, this happens to be Chinpui's favorite dish.
Eri's sweet-natured father is constantly henpecked by his domineering wife, who rules her domain with an iron fist.
Neither of Eri's parents seem to notice the stream of talking animals flowing through the household (although her father is initially freaked out by the "weird blue monkey" in the living room).
- It's also worth noting that Mrs Kasuga absolutely hates door-to-door salesman, considering them less human than any of Eri's unearthly visitors.
Wandayuu always announces his arrival by shouting "congratulations!!" and showering Eri with confetti and streamers. The resulting mess requires a miniature black hole to remove it.
Eri really likes Uchiki-chan, but just can't quite spit it out. For his part, Uchiki is just too darned thick to notice they're way past the friendship zone.
Whenever Eri finds herself in a jam, Chinpui agrees to help out if she promises to marry Prince Lulealv. Eri adamantly refuses, but Chinpui helps her anyway.
Alien visitors seem to have no concept of privacy, frequently turning up while Eri is taking a bath (CF Shizuka in Doraemon).
Eri turns Badass Normal when anyone threatens Uchiki-chan.
Chinpui turns Badass Abnormal when anyone threatens Eri. We're talking Galactus mode here, folks.
Except, of course, when he's confronted by anything that even vaguely resembles a cat - even one of Eri's stuffed animals.
Whenever one of Wandayuu's Rube Goldberg contraptions malfunction, poor old Mr. Kasuga always seems to wind up with egg on his face.
Any photograph taken of Eri will inevitably turn out to be a Panty Shot or a nude. This is because both the interstellar paparazzi and the universe in general are determined to embarrass her.