Books

If its for older kids (8-12 and able to read reasonably well) you could check out the Warriors, Survivors, and Seekers series by "Erin Hunter". This is not an actual author, but a group that churns out tons of books from the standpoint of cats, dogs, and bears.

My kids adored the Warriors books (fantasy stories where all the characters are cats) and they are still into fan fiction as mid-teens. My wife and I read the first one with them when they were around 5-6 years old and it was so awful we refused to ever read another with them again. I think my oldest learned to read about that time just so she could keep reading them after that. At this point I think they own 20-30 of these books and enjoyed them immensely.

This week my kids both started reading Journey to the West, which is a set of 16th century Chinese novels written by Wu Cheng'en. I don't think it is quite what you're asking for, but I gather that a significant portion of it revolves around Sun Wukong, the Monkey King. I think they bought this Kindle version for $4. Apparently the Monkey King is the character in the recent game Black Myth: Wukong, which has made the book popular again.

Watership Down by Richard Adams deserves a mention I think. It's not exactly a series, but it did get a sequel. Richard Adams also wrote The Plague Dogs and Shardik. Shardik doesn't actually take the POV of the animals, but Lord Shardik is a mythical bear that is kind of a main character. I haven't read The Plague Dogs yet, and only learned about it while checking my spellings for this comment, but everything else.by Adams that I've read has been amazing.

Redwall book series

But I read them back when I was a kid. Not sure how it holds up to adult readers

Watership Down by Richard Adams

Only adult one I can think of is Tailchaser's Song by Tad Williams (cats). There's a ton of these for kids, though; here's a few I've read:

• Redwall series by Brian Jacques (forest critters; I found it repetitive after the first few, but ymmv)
• Mrs. Frisby and the Rats of NIMH by Robert C. O'Brien (rats)
• Stewart Little by E.B. White (mouse)
• Charlotte's Web by by E.B. White (pig)

Edit: Sorry, I derped on the scifi/fantasy/action aspect of the request; the E.B. White books don't fall into that category.

"The children of time" by Adrian Tchaikovsky might be something like what your looking for.

Sci Fi with spiders point of view. Highly recommend if you don't have arachnophobia.

A Night in the Lonesome October - Roger Zelazny... this is almost exactly what you are asking for.

Iron Druid chronicles has a small bit of it.

White Fang and Call of the Wild are classic examples of it.

Hollow Kingdom by Kira Jane Buxton is amazing, although the follow up isn't as good.

Adrian Tchaikovsky's Children of Time is also amazing, though, again, the follow up isn't as good.

If singular books are OK, there's Ka: Dar Oakley in the Ruin of Ymr by John Crowley.

I could give more titles because I love books from the animal perspective, but these are my sci-fi/fantasy recs. I also second Watership Down.

Fifteen Dogs kind of fits. It's about a bunch of dogs that gain human intelligence and what they do with it.