Not actual radio-like telepathy like in sci-fi stories, but an inbuilt capacity to actually experience what our brains think other people are experiencing.
One of the classic experiments like this is to get a subject wearing goggles to identify with a mannequin. Of course this is artificially induced; we didn't evolve in a world with 3D goggles and cameras. But there is a condition called "mirror-touch synesthesia" in which this occurs naturally, in which people spontaneously experience what someone else is experiencing.
The parallel element I see is the brain somehow generates a sensation without an appropriate physical input, and the phenomenon of mirror touch synesthesia suggests to me this isn't just a curious bug in our brain architecture. The 1.6% of people who report spontaneous mirror synesthesia also score higher than the general population on measures of empathy. I suspect it may also be linked in some way to our ability to learn by copying what others do.
This is a really exciting time in neuroscience, and synesthesia seems like an interesting target for DIY brain hackers. Mirror-type synesthesia particularly so because it's easy to induce. The rubber hand illusion is probably the easiest dramatic effect to produce at home.
The meat is rotten, but the booze is holding out. Computer translation of "The spirit is willing, but the flesh is weak."