Plateau Eyes is a unique power exhibited by Matthew Keller in A Gift from Earth. It's a specific form of control over a person's iris: When Matt wanted to be left alone (or got scared), his power caused the irises of people looking at him to contract, so that he effectively disappeared from sight (and from thought). As Matt gained control over his power, he found he could use it to expand someone's iris as well, making him fascinating (to women, for example).
The original definition of "Plateau Eyes" is a trance-like state induced by staring over the edge and 40 miles down into the seething mists of the thick atmosphere of the planet Plateau.
For Further Reading: A Gift From Earth
Gil Hamilton was an asteroid miner in the Belt before he came back to Earth and joined the ARM. An accident in the Belt sheared his right arm off at the shoulder. While awaiting a transplant, Gil noticed the "phantom itch" that many amputees describe, namely the sensation that the missing limb is still there. But Gil quickly discovered (quite by accident) that his arm was still there, in a sense. Limited telekenesis gave him the ability to manipulate small objects, such as cigarettes and shot glasses, as if he'd never lost the arm in the first place. What's more, he found he could reach through walls and even into video screens to feel and manipulate objects on the other side. This unique talent helped him on many occasions during his years hunting down organleggers for the ARM. Gil's "arm" has two limitations: (1) it's not very strong--a shot glass is the largest thing he can handle in full gravity; and (2) it's limited to the reach of his own "real" arm.
It should be noted that the ARM has always had a special place for psychics and others with "talents." One of Gil's co-workers, for example, was a psychic named Julie, who could read the minds of ARM agents and thus help keep track of them--but only if she loved them.
For Further Reading: Flatlander
Larry and Judy Greenberg met when their university conducted psychic evaluations. Larry showed a strong talent for mind-reading and Judy displayed precognative abilities--she seemed to know what was going to happen before anyone else did. It was only natural that they should be married. Judy's talent never evolved into much, but with the help of modern technology Larry was able to read human and even dolphin minds. Each contact with a foreign mind left Larry with a new set of memories. He became skilled at separating new dolphin and human personalities from the "real" Larry Greenberg, but when he read the mind of Kzanol the Thrint, a powerful telepath with the ability to control minds, he was overmatched and for a while Kzanol's personality ran rampant in Greenberg's brain. Greenberg won out in the end, and he and Judy followed a lifelong dream to emigrate to the colonies.
For Further Reading: World of Ptavvs
Thrints like Kzanol used to rule the Milky Way, 1.5 billion years ago. Their rule was absolute because they possessed the Power, an irresistable form of mind control. They didn't need to hunt, as they could summon food animals to walk up and wait patiently to be killed and eaten. When a space-faring race touched down on the Thrint homeworld, they instantly became the first non-Thrint slaves and the Slaver Empire was born. In the face of such power there could be no compromise, and the Thrints and all other advanced life in the galaxy were exterminated in a galaxy-wide revolt. Today the species known as Grogs possess a form of mind-control similar to that of the Slavers, and there is a theory that they are in fact devolved from Thrints who somehow survived. The Grogs claim no knowledge of Slavers, and have found ways to be useful throughout the colonies of Known Space. Whether they're telling the truth or not is anyone's guess.
For Further Reading: World of Ptavvs, "The Handicapped"
Kzin Telepaths are a unique caste within the warlike Kzinti species. They're the product of a long line of experimentation, and gain their power only through an injection of sthondat-lymph extract that drives 99 out of 100 mad. The telepaths who survive have a limited mind-reading ability (provided the have access to the drug) and are pressed into service throughout the Patriarchy, where they are treated with contempt even as they are relied upon for hard military and political intelligence.
For Further Reading: "The Warriors," "Fly By Night"
Niven himself doesn't believe in Psychic Powers. In the essay "Niven's Laws" he writes "Psi and/or magical powers, if real, are nearly useless. Over the lifetime of the human species we would otherwise have done something with them." Thankfully, Larry suspended his disbelief long enough to create some of the most memorable and unique psychics, mind-readers and magicians in modern fiction.