If you're looking for anime similar to Araiguma Rascal, you might like these titles. All recommendations are made by Anime-Planet users like you!
One day, a young kitten was on a walk with her mother and siblings; but soon she became separated from her kin. Struggling to find her way home, the kitten soon ran into a young boy named Yohei and his mother; and out of pity, the duo takes the kitten home with them. Unfortunately they discover that they are unable to keep pets in their home, and thus begin a quest to find her a new place to live. From playing with shoelaces to being washed, the cute kitten named Chi will have fun and get to know her new family – though all she really wants is to make it home to her feline mother.
Adorable creatures, and ones that can sometimes get into trouble.
While Rascal moves on to the story of the young boy, it does spend a great deal of time with the raccoon as a youngin at the start of the series. Chi centers more around the cat than the family that owns the cat, but the harmless vibe is there for both. (both are Family friendly)
Rascal the Racoon, was an odd title a club of mine translated. It might be a bit hard to find a sub, but there is a French and Spanish version available on the net if you speak those languages.