Great thanks to Paul P, who posted the link to biologist and author Rupert Sheldrake's Google Talk in the comment thread to another article.
Sheldrake has been conducting research into the hypothesis that our minds extend beyond our skulls, the way a magnetic field extends beyond a magnet, or a gravitational field extends beyond the planet.
Ninety percent of the population have experienced the feeling that someone's looking at them, turned around, and someone is.
Sheldrake relates how a security guard told him he'd been instructed by an FBI trainer to stare at people through the monitors of his bank closed circuit cameras, if he saw them doing something they shouldn't. They usually stop. He does this almost every day, and said this is widely known in the security industry. Taken for granted, even.
Detectives know not to look at someone they're shadowing directly, or they'll turn around.
British secret service operatives are trained not to stare at someone they're about to stab in the back, for the same reason.
There's very little scientific research into these phenomena, even though they're widely experienced.
Wildlife photographers and hunters have reported that animals often know when they're being looked at.
Jim Corbett, a famous tiger hunter in India during the British raj, wrote of having his life saved multiple times by the sensation of hairs standing up on the back of his neck alerting him to the presence of an unseen tiger.
Any prey animal who was sensitive to these feelings would have a strong adaptive advantage. They'd escape more often.
Sheldrake believes this phenomenon isn't supernatural, it's natural. We don't possess this sense because we're more evolved than animals, but precisely because we are animals.
Any cat owner will tell you their cat just knows when it's time go to the vet, and disappears. Sheldrake phoned 65 vet clinics in London and asked if they ever had trouble with cat owners missing appointments. Sixty-four said "all the time," and the sixty-fifth said this was such a problem that they'd stopped making appointments for cats altogether.
Dogs often know when their owners are coming home, even when they return at different times. Sheldrake set up experiments in which dog owners would be given a randomized signal by pager, when they were at least five miles away. They'd travel home by transit or taxi, so there was no chance the dog was hearing a familiar car engine. The area near the front window was filmed throughout the day with a time-coded camera. Fifty percent of dogs would come and wait at the door when their owners were on their way. The most sensitive would even wait by the window when their owners had simply decided to come home.
Sheldrake had a skeptical colleague repeat the experiment, who came up with the same results.
There's a great deal more to this Google Talk - the telepathic bond between mothers and their babies, studies looking into people thinking about someone seemingly out of nowhere, and then suddenly having that person phone, or email, the reaction speed of flocks of birds and schools of fish - and I highly recommend watching it.
Sheldrake details some of his work on this field on his website and in his various books, such as The Sense of Being Stared At and Dogs That Know When Their Owners Are Coming Home and Other Unexplained Powers of Animals: An Investigation. Divergences from our standard understanding of science should indeed be approached with an open mind and a critical sense of discernment. I'm looking forward to reading more about his research and ideas.
