Mouse is Harry's extraordinary dog, first appearing in Blood Rites and accompanying Harry on his cases in all subsequent novels. He's is a "temple dog," a celestial scion of the Foo Dog (divine spirit guardian)1 and a mortal canine. So mouse is only partially mortal and it explains Mouse's exceptional intelligence and perception as well as his more than a dog supernatural powers. Mouse is fiercely loyal to Harry and has saved his life on many occasions. He is exceptionally intelligent and seems able to detect dark energy, often sensing it before Harry himself. Mouse is in fact an authentic temple dog though it is not clearly spelled out until bob confirms the status and the powers in book nine "White Knight" of the Dresden Files Series.
Physically Mouse is said to resemble a Caucasian Shepherd Dog, although a Tibetan Mastiff would seem to fit the descriptions of him at least as well (not to mention being quite appropriate for his intended role. Harry's alternative classifications such as "Wooly Chammoth" "Dogasaurus Rex" and "Westhighland Dogasaurus" should be considered humour rather than taxonomy.
Mouse's Early Days
In the beginning of "Blood Rites," Harry was hired by Tibetan monk Brother Wang to rescue Mouse and the rest of his litter, who had been kidnapped by a black sorcerer and his pack of demonic, flaming-poo-throwing monkeys. However, being the troublemaker of the litter, he ended up stowing away in the Blue Beetle during the trip back to the airport to meet Brother Wang. With no way of reaching the monk when he discovered the mistake, Harry ended up adopting the puppy.
Harry named him Mouse because of his quiet temperament, grey coloring, and small size. However, he grew to be enormous, and Harry suspects he may not even be full-grown. He is compared to the Caucasian Ovecharka Mountain dog, but he's large even for the breed, with his head easily reaching Harry's waist.
Mouse's Powers and Abilities
In "White Night," Bob finally gives us a breakdown of the stories and myths behind the "temple dog". Mouse may or may not possess the abilities listed, which include detecting of dark energy, and dark spirits, overt guardianship of owner and family, protection of religious shrines, give warning to a small county, and finally above Lassie type intelligence. if you want some specific on exactly what the verified powers of mouse are according to Bob, Harry's magical spirit of memory and intellect, then check out page 124 to page 125 in white knight (paperback edition) where it is all laid out. There is also some interesting side notes that confirm that they are formidable as "Ancient Mai created some temple dog statues to assist wardens in maintaining security. While the abilities listed here are the ones that Bob states as being confirmed by multiple sources as being true, the description of mouse and the powers he may have is left open as there are other possible powers that bob does not list as they are not confirmed by multiple sources. But essentially Think of Mouse as the Lassie outfitted for the super natural world with a whole extra can of large dog whoop ass thrown in.
We have seen that Mouse has often used his intellect to help Harry out in his investigation, and that he has a sixth sense when danger or evil is nearby, even beneath a veil. In Proven Guilty Mouse survives getting hit by a van, with nary a scratch, and seems to gather a flow of energy prior to bringing down a supernatural villain. In White Night, Mouse barks loud enough to warn an entire building of danger, using sound and energy to convey the message. He is also shown to manifest a glowing aura when attacking supernatural beings - possibly some form of enhancement that allows him to overcome supernatural defences.
In Changes, Mouse's intellectual abilities are underlined again when he is recognised as a competent witness (and, indeed a Foo Dog) by the court trying Warden Morgan. This and his arguments with Lea on the road to Chichen Itza strongly imply that he is not just a smart dog, but actually a sapient being in his own right.