If you're looking for anime similar to Fuku-Fuku Nya~n New, you might like these titles.
This story follows the daily lives of a cat named Tama and his cat and dog friends. As their curiosity gets the best of them, they learn enduring values of friendship and teamwork.
What's Michael? Michael is a cat. A cat that is inexplicably attracted to the smell of raw fish, yet horribly repulsed by the smell of toothpaste. A cat that, in a dogfight with a fly, will strafe his master in her sleep. In short, Michael is a cat like any other cat.
Higepiyo is just like any other chick; he's small, yellow, and... has a beard?! With an imposing presence and his constant sighing, it's not surprising that Higepiyo is the last chick left at the festival stand. Luckily for the now-depressed salesman, Hiroshi and his parents decide to buy Higepiyo for their own bizarre reasons. It's only when the family get him home that they realize just how weird this chick really is. From reading the newspaper to attacking the school bullies over a bread roll, Higepiyo is far from your average pet. Now Hiroshi and his parents must adapt to living with this food-crazed, talking chick - that is, if they can stop living in fear of their new pet! They just have to remember that while Higepiyo may not be cute, he may have a beard and he may ask for a second helping of curry, he's still a chick just the same!