If you're looking for anime similar to A Man and His Cat, 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.
The daily life of a household that has two cats: Azuki and Daizu. Azuki and Daizu belong to an office worker in her 30s who loves cats. The owner lives with her father, mother, grandfather, and older brother, the latter of whom the cats call "Megane" (Glasses). Megane adopted a Shiba Inu dog named Mamenosuke after Mamenosuke's owner died. Mamenosuke grew up around cats so he actually thinks of himself as a cat.
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.
A hard-working way-too-cute dog and a scary-faced but lovable cat. Living with them makes every day fun. Their owner's days are filled with laughter and sentiment. Are you a cat-lover? A dog-lover? Or both? This anime is a present for the people out there who love both dogs and cats so much they can't choose.