Foxes were four legged wild canines that lived near the woods and wilds surrounding the outskirts of the Shire. They were not known to be menacing, and probably avoided Men and Hobbits.
The most famous of the mention of foxes was when they approached the company of Hobbits as they slept in the woods after they left the Shire. It was narrated of how the fox thought it was very queer to see Hobbits asleep in the woods, but the fox didn't stay to find out anything more. This fox seems to have possessed sentience, although it's not clear if all foxes in Middle-earth did, and this may have simply been personification. Later, the Hobbits see another fox, although it is unlikely that this is the same one they had seen in the woods.