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Tendonman from Anpanman. He's the youngest, most traditionally cute-designed, and loudest member of the Donburiman Trio, and was the first Keet of the series, being introduced in the first episode before the other members of the trio.
The Sogyo no Kotowari twins from the Unknown Tales arc certainly fit the bill.
A very early installment had a boy who fit this trope who had literally been turned into a parakeet.
Although, fitting the trope personality-wise is really just implied until we see him again in the Soul Society, since his story is probably one of the truly darkest in the entire series.
A somewhat more mild version is Alistair Cornwell alias Stear from Candy Candy. He's very cheerful, energetic and a teenaged Absent-Minded Professor, but he can also be serious when needed and ultimately falls victim to a truly tragic death in World War I.
Kanda Yuusuke from A Devil and Her Love Song tends to act pretty genki at times. He's not small or hyper-active, but seems to be the cheeriest out of the bunch. He holds a bright personality & tends to be overly friendly, which annoys his best friend Meguro sometimes.
Micchi of Kamichama Karin takes this to whole new levels. His interaction with the rest of the main cast comes dangerously close to flirting (both with Karin and Kazune). This is even though he's a year older and One Head Taller than either of them.
Mizuki from Kamisama Kiss. He's a little older than most examples here but otherwise fits the trope perfectly.
Yogi from Karneval can be overdramatic and flamboyant one moment, then more serious than his "rival" First Ship's female fighter the next. He's not small and cute, though; just loud and cheery. It annoys the heck outta Ineffectual Loner Gareki when his sunshiny personality is directed at him.
In Mahou Sensei Negima!, a good portion of the male student body falls under this. The final event in the previous year's Mahorafest was a game of tag. Which they aren't repeating this year because there were too many injuries.
Negi also qualifies when he's able to get away from his Training from Hell and responsibilities as a teacher. When he acquires a time machine during the festival arc and realizes he has enough time to do everything, he goes right into adorable-kid mode.
His first impulse was to use the time machine to go back and see the dinosaurs.
Nabari No Ou: Gau, who is hyperactive, passionate and regularly loud. Yukimi's nickname for him is "Tenpa-kun", which is derived from the slang term "tenparu" (lit. "about to blow a fuse").
Naruto in Part I. It is toned down in Part II, where he matures. This is lampshaded in the Shippuden anime when Naruto and Sakura do an Omake beside their younger selves, and Naruto can't believe how hyper he used to be.
Akatsuki member Tobi is also hyperactive, especially in the Anime version. When he reveals himself to be Madara Uchiha, though, he drops the act. Then he turns out to REALLY be Obito, aka the "Naruto" of Kakashi's genin team.
Not to mention Rock Lee and Guy, who are so energetic it even makes Naruto pause at times.
Of all people, Senju Hashirama, the First Hokage, has sides of this, especially next to his stoic brother.
Tony Tony Chopper from One Piece to a certain extent.
Mizushiro Hizumi from Spiral is "the Devil"... a very, very cheerful and cute one. When he isn't being murderous and/or unbearably angsty, that is - he'll switch between all three moods in a matter of seconds.
Trigun: Vash the Stampede falls into this mode as a part of his Obfuscating Stupidity, but he also seems to take some comfort in the act, especially while enjoying his donuts, which is a sure trigger for it.
Haru from Tsuritama. Cute, eccentric, and least a third of his dialogue is yelled.
Uta No Princesama heroine Haruka Nanami's singing idol Hayato is this. Or rather being keet is his image for the fans.
Kimihiro Watanuki in Manga/xxxHOLiC is so Keet that eventually Doumeki stops bothering to tell him to quit being so loud and simply covers his ears when Watanuki inevitably gets overexcited. Or annoyed, which happens more often in Doumeki's vicinity.
He steadily starts growing out of it due to Character Development, and then abruptly ceases to be this completely when a certain major character dies.
The concept itself is horribly, horribly deconstructed by Kiyoshi Mitarai, though, since he has the looks of a keetand the voice for it but all it gets him is to be horribly bullied, which later mskes him lose his faith in people and join Sensui in his quest...