Philosopher and psychologist William James was one of the first psychical researchers who worked on a variety of paranormal and mesmerist cases. Respected in his field, and still studied today, James remained deeply skeptical with regards to psychic powers and paranormal realities. Like Thomas Edison and Freeman Dyson, James can't really be said to have been a paranormal believer, but all three of these men did devote considerable energy and resources into researching it....others followed up on their work and came to widely varied and controversial conclusions.
1Carl Jung's Synchronicity and the Scarab Beetle
Jung was heavily affected by an experience with a patient, during which the patient randomly mentioned a dream of hers in which she was given a golden scarab. At that moment, a beetle rapped at the door to Jung's office and when he opened the door, a golden scarabaeid beetle flew into his office. He captured the beetle in his hand and presented the golden scarab to the patient.
2Wolfgang Pauli and the "macro-psychokinetic" phenomenon
Most relevant to our discussion here is the fact that Pauli became the namesake behind something called the “Pauli effect,” which supposed that humans could disrupt electronics through some kind of "macro-psychokinetic" phenomena. The "effect" name became attributed to Pauli because of the inordinate number of times that his presence seemed to have broken experimental equipment. It is said that his friend, the experimental physicist Otto Stern, even banned Pauli from his lab for fear that his equipment would be damaged.
Pauli himself explained his beliefs somewhat esoterically when he professed to believe in “the existence of relatively constant psychic contents that survive personal ego...All we can observe is their effect on other living people, whose spiritual level and whose personal unconscious crucially influence the way these contents actually manifest themselves.”
Basically, Pauli believed in psychokinesis before there was an agreed upon name for it.
3Anthropologist Margaret Mead believed in psychic powers
Controversial in many ways, Mead was also an Anglican Christian who believed strongly in psychic powers, though she referred to people who possessed such powers as "sensitives."
Here's a video of her discussing her beliefs in her own words.
4Nobel Prize winning physicist Brian Josephson and parapsychology
He claims that quantum entanglement leaves open the possibility of consciousness affecting the physical universe through telepathy, psychokinesis and transcendental meditation.
Mainstream peers largely reject his theories, especially his ideas about water memory and cold fusion.
5Dr. Fred Alan Wolf: Intersections of matter and consciousness
His more controversial quotes include:
"There is enough in the nature of the way the physical universe is constructed to indicate the presence of something called soul."
"the soul, which is non-physical and therefore not confined by movements in the material world, can travel faster than the speed of light...
So at the time of death, or during a near-death experience, it may very well be that the person transitions from the material world--that operates at speeds less than the speed of light--to a world that operates faster than light speed."
6Dr. Amit Goswami and What the Bleep Do We Know!?
His most famous work is solving the quantum measurement problem in the famous observer effect in quantum physics.
“Consciousness is the ground of all being. In this view, consciousness imposes ‘downward causation'. In other words, our free will is real. When we act in the world we really are acting with causal power. This view does not deny that matter also has causal potency — it does not deny that there is causal power from elementary particles upward, so there is upward causation — but in addition it insists that there is also downward causation. It shows up in our creativity and acts of free will, or when we make moral decisions. In those occasions we are actually witnessing downward causation by consciousness."
7Dr. Stuart Hameroff and the Quantum Soul
Hameroff believes his theory can help explain the incredibly frequent incidents of near death experience, when people seem to leave their bodies after the heart has stopped beating and then return with a head full of otherworldly images. One of the most recent and noteworthy near death experiences happened to a lifelong atheist, Dr. Eber Alexander.
8Dr. Eben Alexander's "Proof" of Heaven
Alexander claims to have visited heaven in a near-death experience. His experience is documented in his book Proof of Heaven: A Neurosurgeon's Journey into the Afterlife, which concludes that life does not end after death, that there follows the resurrection of the mind into a different state.
Alexander defended himself against his critics by writing the following:
“Critics have maintained that my near-death experience, like similar experiences others before me have claimed, was a brain-based delusion cobbled together by my synapses only after they had somehow recovered from the blistering weeklong attack. I also experienced that transitional period, when my mind began to regain consciousness: I remember a vivid paranoid nightmare in which my wife and doctors were trying to kill me, and I was only saved from certain death by a ninja couple after being pushed from a 60-story cancer hospital in south Florida. But that period of disorientation and delusion had absolutely nothing to do with what happened to me before my cortex began to recover: the period, that is, when it was shut down and incapable of supporting consciousness at all. During that period, I experienced something very similar to what countless other people who have undergone near-death experiences have witnessed: the transition to a realm beyond the physical, and a vast broadening of my consciousness. The only real difference between my experience and those others is that my brain was, essentially, deader than theirs.”
Additional "eminent" scientists who believe(d) in the paranormal include: Alfred Wallace, Ron Pearson, Charles Richet, George Meek, and others....it sort of depends on your definition of 'eminent'. Here's a good list from throughout history....