Well, let's see, OTGM...
I haven't read any of them, but I know plenty of kids who like Kenneth Oppel's Silverwing series (bats).
Would he like some of the E. Nesbit books? They're about children, but some have "critters" (the Psammead, the Phoenix, various dragons).
Oldies but goodies are some of the Albert Payson Terhune dog books. (Lad: A Dog is the one most people seem to know).
Is he too old for the Narnia books?
The Bunnicula series is likely too young for him, as is probably the Freddy the Pig series. Still, there are lots of both of them--and sometimes it's fun to read younger stuff.
Several of the Oz books might suit. There are some talking animals in the Tolkien books, too.
Would adult books like Animal Farm or Watership Down or The White Bone be too intense for him?
Does he like horses? There are lots of horse series, not all of them girly--I remember liking Mary O'Hara's books (My Friend Flicka is the first one). The Walter Farley Black Stallion series is very good.
Lots of animals in Rudyard Kipling, of course, though those are not series books.
Farley Mowat is grand (The Dog who Wouldn't Be, Owls in the Family).
The Cressida Cowell series that kcab mentioned earlier on this thread is fun (Vikings and dragons).
We all liked Christie Harris's Mouse Woman series. You might look for other volumes of folk tales, too (Aesop, Anansi, etc.).
Sheila Burnford's "The Incredible Journey" is great, but not part of a series. Other great talking-animal but non-series books are Mrs. Frisby and the Rats of NIMH, and The Voyage of QV66. Oh, and there's Lloyd Alexander's Time Cat, which is good.
Of course, the Tintin books all have Snowy (the dog).
Hmmmmmmmmmmm..........
ETA: Someone I know recommends Avi's Poppy series (I don't know them myself).
Another thought I had, though not quite in the same vein as most of the rest of these, are the James Herriot books.
Oh, I know, JP Martin's Uncle books (elephant).
