are there other races of humanoid beings in middle earth

just dickfors.

They actually have a race of "vampire" type creatures, but they're rare and difficult to find.

Well, I'm not sure if this answers your question, but there was a tribe of primitive, dwarf-like (in terms of height) men called Drúedain who lived in Drúadan Forest. Yes, they were human, but I bring them up because they played a key role in RotK but were not shown in the movie. They and their chieftain, Ghân-buri-Ghân, helped Théoden and the Rohirrim travel through a secret pass to avoid an army of Orcs and reach the Pelennor Fields. Afterwards, when Aragorn was king, he decreed that the Drúadan Forest belonged only to the Drúedain and outsiders without permission to enter were forbidden. The Drúedain struck me as being analagous to the indigenous peoples of the Americas (minus the height thing).

You forgot Ents.

Vampires were mysterious bat-like creatures in the service of Morgoth and of Sauron. The only vampire whose name is recorded in the annals of Arda is Sauron's messanger, Thuringwethil.

Giants and the mewlips. We could add some undead, such as werewolves, to humanoid races.