There are many such species.
To name a handful:
Note that Q and Changelings usually take humanoid form when we see them on screen. The Silver Blood may not count as a non-bipedal intelligent species because it did not gain its intelligence until it copied humanoids (at which point it also copied their bipedalism).
Don't forget Spock's Sehlat, I-Chaya. And the Tholians. The Gorn in ST:ENT "In a Mirror, Darkly" (but not ST:TOS "Arena") is questionable. Data's cat. Species 8472.
And the Horta
The canon reason why most aliens on the shows are bipedal humanoids is due to the genetic seeding of the ancient humanoids, who planted DNA on many planets that turned into prominent space-faring species. The real reason is that it's too expensive to turn actors into non-bipeds or use CGI characters frequently, but the makeup artist can slap a little sculpting clay and paint on a person until they look reasonably unique.