The first creatures we see in the film are definitely not familiar animals. I usually describe them as "ant men" but I'm not sure if that's what was intended. Zenobia summons three ant men from a fire to battle Sinbad and his men in the exciting early scenes of the film.
Zenobia transforms Prince Kassim into a baboon. Harryhausen has said that the filmmakers originally considered using a real baboon but that it wasn't possible to find one that could be trained appropriately. Frankly, I'm glad they let Harryhausen create one because it showcases how incredible his art has become. Kassim's movement is flawless. It's easy to forget that you're watching an animated character.
Unwilling to do menial labour, Zenobia fashions a bronze giant called Minoton to do her heavy lifting. Minoton is actually a combination of stop-motion and an actor in a suit. He was played by Peter Mayhew in a couple of scenes. Minoton is one of the classic and unforgettable characters most associated with Harryhausen.
One of the animals I mentioned above is a giant walrus that Sinbad and his crew encounter on their way to Hyperborea. He doesn't get much screentime and it's sort of a strange encounter but, nevertheless, well-executed.
One of Harryhausen's most sympathetic creations is Trog, a larger than life troglodyte encountered in Hyperborea. He's extremely life-like and his facial expressions give him a really strong character. You really feel like you can see Trog thinking. Apparently, Trog was originally going to be an actor in a suit. Harryhausen wanted to use animation to give him more of a fantasy, pseudo-reality feeling. I think it works!
Finally, another of the animals I mentioned, a sabretooth tiger. All three of Harryhausen's Sinbad films include a climactic battle between two of his creations. In this one, brave Trog faces the tiger and allows Sinbad's party to escape.
Be sure to check out Ray Harryhausen's official website for more great info on the master.