Yes. There's a Jewel Pet that's the 'paw up' puppy.
Three of the four from Splash Happy Pups don't move. The bulldog is a squirt toy but I don't think that counts.
The Beethoven puppies and Missy.
Some of the dress-up dogs, there's another squirt toy and a flocked dog.
The Yorkie from the hair pets line.
I'll add more as I think of them.