If you're looking for anime similar to Puri Puri Chii-chan!!, you might like these titles.
Momoko Sakura is an elementary school student who likes manga and the popular idol Momoe Yamaguchi. She is often called "Chibi Maruko-chan" due to her young age and small size. She lives together with her parents, her grandparents and her elder sister in a little town. In school, she has many friends with whom she studies and plays together everyday, including her close pal, Tama-chan; the student committee members, Maruo-kun and Migiwa-san; and the B-class trio: 'little master' Hanawa-kun, Hamaji-Bu Taro and Sekiguchi-kun.
One year ago the pint-sized Memoru and a few hundred of her people crash landed their spaceship on Earth. They've since been living on a lake island, with only the large objects that wash ashore as their knowledge of humans. One day, young Memoru and her friends head towards the sound of beautiful music and find a huge house with an equally huge human girl inside. Memoru wants nothing more than to be this girl's friend, but she soon discovers that the girl is sick. Heartbroken, Memoru cries on her would-be friend's face, miraculously healing her - and thus their friendship begins. Together with her people, Memoru experiences life on Earth with a smile and meets plenty of new companions along the way.
Gou-chan arrives on earth in search of the "heart plasma" that will restore peace to his home planet EX Panda. He meets a human girl named Moko, who lives on a farm with her grandfather, and several strange animals called "Chinjuumin." They pass their days enjoyably, but trouble begins when humans invade the forest home of the Chinjuumin looking to capture them. Meanwhile, Moko's family life gets complicated when her grandmother arrives from the city.
In the future, aliens coexist freely with mankind on Earth. One such alien is NieA, a lazy yet spirited girl who wastes away her days while living with the studious Mayuko. And life isn't easy... Mayuko is always short on food money, the spa where she works is about to go bankrupt and Mayuko's alien-crazy friend Chiaki is obsessed with NieA.
Umika is a sweet yet shy high school girl. She has trouble speaking to others and dreams of having a friend from another planet. But her lonely school life takes a cosmic turn when she meets transfer student Yu, an alien with telepathic powers! The two become close and promise to go to space one day. So, they decide to build a rocket and shoot for the stars, making new friends along the way.
Poor Chow Ti lives in a demolished house with his son, Dicky. One day he heads to the junkyard and comes back with a green blob that turns out to be a cute, magical alien.
Takashi Horimachi is an ordinary curious fifth grader attending "Anytown" Elementary School. One day, a very unusual transfer student named Taro Tanaka joins Takashi's class. Takashi and his classmates have never encountered anyone quite like Taro before. He is blue, has huge glowing eyes, pointy ears, a smooth bald head and one horn. Takashi, obsessed with trying to figure out this strange new visitor, attempts to track Taro's every move; and in the process he continuously falls victim to Taro's hilarious assortment of cosmic jokes and traps.