A couple quick stories:
1. HHKarmapa XVI was going to do a Vajra Crown ceremony in L.A. Everybody had taken their seats, and there were a number of crying children of various ages scattered around the hall. The very loud Tibetan horns announcing the approach of HHK started blaring, but the children could still be heard over the horns.
HHK enters, takes his seat, and is offered the Crown. He paused for a moment and then placed it on his head. The moment it touched his head every child in the audience stopped screaming simultaneously. And I do mean simultaneously. It wasn't like it took 30 seconds for the crying to wind down. It just stopped, for all dozen or so kids.
2. Kalu R. came to Santa Cruz to give a talk. The afternoon before the talk he went for a walk on the beach, and turned down the Aptos pier. There were about 50-60 people with him, varying from suits and ties, to hippies, to college students, and of course some monks.
A fisherman got a seagull tangled in his line. One of our guys, Yeshe, untangled the gull and presented it to Rinpoche. The gull was in mortal terror, flapping one wing frantically and trying to peck anybody and anything it could. The second wing was immobilized. Rinpoche was reciting "om mani padme hung" and then touched the bird. Instantly the bird stopped moving, then cocked it's head. Now gulls have eyes on both sides of their head and can see 360, so I can't say that he was looking at R. per se, but it seemed like it to me. In any case, whatever was going on between Rinpoche and the gull made the gull completely forget it's mortal terror.
After a moment or two Rinpoche withdrew his hand and motioned to let the gull go. The gull started moving again, but not frantically. It just wanted to let go, but it still hadn't moved it's wing. Yeshe took it to the side of the pier as if to throw it over the side, when somebody said, "Don't! It's got a broken wing!" Yeshe threw it anyway, and it did a glide down to the beach. I guess Yeshe's fingers were pinching the wing, but I don't know that.
That night Kalu R. gave the standard talk on "The Precious Human Rebirth". There was no mention of the incident with the gull, even though there were 50+ people there that would have vouched for it.
Those were two very public incidents. Lots of witnesses. I was there for both of them, so these are first hand accounts, not just rumors. Such people do exist, or at least they did exist in the recent past, it isn't just scriptural mythology. Whether there are such people in the future remains to be seen--and it is up to us.