There are actually two famous anomalous issues surrounding Wolfgang Pauli. There is the "Pauli effect", mentioned in the YouTube video below, which is more fully described by Michael Talbot in "The Holographic Universe":
"Jahn and Dunne think their findings may explain the propensity some individuals seem to have for jinxing machinery and causing equipment to malfunction. One such individual was physicist Wolfgang Pauli, whose talents in this area are so legendary that physicists have jokingly dubbed it the "Pauli effect." It is said that Pauli's mere presence in a laboratory would cause a glass apparatus to explode, or a sensitive measuring device to crack in half. In one particularly famous incident a physicist wrote Pauli to say that at least he couldn't blame Pauli for the recent and mysterious disintegration of a complicated piece of equipment since Pauli had not been present, only to find that Pauli had been passing by the laboratory in a train at the precise moment of the mishap! Jahn and Dunne think the famous "Gremlin effect," the tendency of carefully tested pieces of equipment to undergo inexplicable malfunctions at the most absurdly inopportune moments, often reported by pilots, aircrew, and military operators, may also be an example of unconscious PK (psycho-kinetic) activity."
The anecdote that goes neck and neck with the "Pauli effect", however, is the infamous story of Pauli and the "fine structure constant". It was made into a book by Arthur ! Miller, entitled: 137: Jung, Pauli, and the Pursuit of a Scientific Obsession.
But, I'm going to cut to the chase and call upon F. David Peat to, once again, inform us. The story is short and ends badly.
"One of the most curious of these stories about Pauli concerns the number 137. One of the great unsolved mysteries of modern physics is the value of the fine structure constant, for while the other fundamental constants of nature are all immensely small or enormously large, this fine structure constant turns out to be a human-sized number. This number l:37 and its place in the scale of the universe particularly puzzled Pauli and continues to challenge physicists today. It was a mystery that Pauli was to take to his death. For on being admitted into the hospital, the physicist was told that he was being put into room 137. According to one version of this story, on hearing of his room number, Pauli said: "I will never get out of here." The physicist died shortly after."
- F. David Peat, "Synchronicity: The Bridge Between Mind and Matter"