I don't recall that happening the The Hobbit, but when Sam puts on the Ring in the Lord of the Rings, he is able to understand the speech of Orcs.
He heard them both clearly, and he understood what they said. Perhaps the Ring gave understanding of tongues, or simply understanding, especially of the servants of Sauron its maker, so that if he gave heed, he understood and translated the thought to himself.
This is from the "Choices of Master Samwise" chapter in The Two Towers. As far as I know, this is the best answer we get, and it seems like the narrator (or rather, the writer of the Red Book) is speculating, but it seems that the Ring does indeed have a "babelfish" effect on its bearer, as you put it. Thought it is presented speculatively, it does make a lot of sense.
When Sauron forged the Ring he put much of his "strength and will" and "inherent power" into the Ring (Of the Rings of Power and the Third Age). That's why destroying the Ring destroyed Sauron. And the understanding of the thought behind speech is one of the powers of the Ainur. In fact, it was something all rational beings in Middle-Earth were capable of. For example, when Elf Finrod first met Men:
Now the Eldar were beyond all other peoples skilled on tongues; and Felegund discovered also that he could read in the minds of Men such thoughts as they wished to reveal in speech, so that their words were easily interpreted.
Or when the Fellowship encountered Galadriel, she read their thoughts even without them intending to speak:
And with that word she held them with her eyes, and in silence looked at each of them in turn. None save Aragorn and Leogolas could long endure her glance. [...] 'Maybe it was only a test, and she thought to read our thoughts for her own good purpose.'
Even Denethor, a Man, was capable of doing so. Gandalf, speaking to Pippin, commenting on Denethor's shrewd questioning:
'He is not as other men of this time, Pippin, and whatever be his descent from father to son, by some chance the blood of Westernesse runs nearly true in him; as it does in his other son, Faramir, and yet did not in Boromir whom he loved best. He has long sight. He can perceive, if he bends his will thither, much of what is passing in the minds of men, even those that dwell far off. It is difficult to deceive him, and dangerous to try.
Tolkien discussed the ability behind this at some length in a manuscript published in the Vinyar Tengwar #39. But at any rate, since Sauron possesses this ability as well, and he poured his power into the Ring, it only makes sense that others wielding the Ring would also have their abilities in that area enhanced.