Carefully controlled experiments with our domestic dog's close relative, the wolf, have demonstrated that they are indeed telepathic. Visual stimuli presented to the alpha pair of a pack will cause the entire pack to look in the immediate direction of the objects although they are completely hidden from the rest of the pack.
Certainly there exists a vast difference in phenotype between Fluffy the wonder-Yorkie and the howling rulers of the Great White North, but these kinds of results give credence to those tales of how the family pet bolts from a sound sleep in front of the fireplace and sets himself on the back of his master's favorite chair to peer out the window anticipating the arrival of the most important person in his life. My mother loved to tell the story of how my boxer, Duke, would immediately drop whatever he was doing (usually something destructive) to watch for me to turn the corner at the top of the street on my way home from school. This same extraordinary canine failed entirely to read my mind when I tried my best to transmit my thoughts on how he must change his behavior or be banned from the family unit he seemed to cherish so much. Despite my most earnest efforts, he was ultimately taken to "a farm in the country" where he could run and would not be so likely to snap the family rump roast from the Sunday dinner table.
It would seem that telepathy in dogs is a sometimes thing; there when it results in some swift reward but completely absent in the pooch totally engaged in behavior whose rewards are more valued and more immediate. The domestic canine has come a long way genetically since the first wolf shared the same space with a human companion. The ridiculous variety of dogs created by our penchant for breeding exactly, precisely what we want has opened a huge gap between wolves and designer dogs. Anyone who has been in close contact with wolves will tell you that they can do virtually anything that a domestic dog can do but that they will not do so on command. It's not a matter of stubbornness or wild pride as some would romanticize. The reason behind this obstinacy is simply that the wolf is far too intelligent to take directions from a creature he does not recognize as superior in any important respect. Wolves do what is important to their mindset which is almost completely involved in survival. The ability for a pack to be quickly aware of what the alpha detects is essential to pack behavior. The pack is a social organism in which each member is part of a single entity that hunts, fights, and flees together. Telepathy is the earliest key that lets cubs know when food is on its way, safely tucked away in mom's belly as she trots home to feed them. Simple observation reveals the young becoming increasingly excited when hunting adults are returning though they are still out of range of any other sense.
Having raised wolves for thirty years, I can go on endlessly with examples both anecdotal and scientific of wolf telepathy. Suffice to say that, as with most characteristics, a bit of the original remains in the domestic dog, and all of the stories told by those maiden aunts celebrating the brilliance of their little Lhasa or pint-sized poodle should not necessarily be dismissed out of hand. It seems a certainty that dogs do develop a psychic bond with their owners along the same line as that established in a wolf pack.
So.... the next time your oldest and most brittle relative spouts off about the mind-reading ability of her little Snookums or your hoary Uncle Ned tells you for the forty-ish time about his long gone genius of a bird dog who could beat a path to a downed pheasant before the first shot was fired..... or your own tiny toy terrier is waiting for you in ambush behind the kitchen counter when you stroll in from work hours early, remember that some species have talents well beyond those of Earth's most intelligent creature.