In the Hobbit, the Trolls, Eagles, Orcs/Goblins, Dragon, some Ravens, and (maybe) the Spiders all spoke Common (Westron). The Wargs, Thrushes, and Crows did not speak Common, but understood Common.
In the scene with the Wargs, Tolkien states that Gandalf understood the Warg's hideous language, and that was why he knew (and the reader knows) what they are saying (pg 93). Similarly, the line of Girion (Bard's ancestry) understood the language of the Thrushes (224), although Balin states that it is too quick for him to understand (pg 230). However, Balin understands the language of Ravens and Crows (there is a scene where Balin comments that the crows are insulting them near the Front Entrance to Erebor, pg 231). Some Ravens (notably Roac) were able to speak the Common tongue (pg 231), and therefore did not need to be translated for Bilbo (who didn't understand the Raven's language).
All page numbers are taken The Hobbit or There and Back Again by J.R.R. Tolkien, published by Houghton Mifflin Company copyright 1997.
Note that the One Ring RPG does not really have an opinion on what language the creatures speak. Thus, we can default to LOTR and the Hobbit for this information, particularly since the One Ring RPG tries very hard to stay true to the Middle Earth that Tolkien created in his books.