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"If that machine could move a birthmark, who knows what else it could do?"
– Hoshi Sato, 2152 ("Vanishing Point")

Barclay suffering from transporter phobia

Transporter phobia was a fear of using transporters, either before one's first use of the device, or consistently over a period of time. Transporter use carried an inherent risk, since transporters disassembled and reassembled matter at the atomic level.

During the 2150s, when transporter technology was still in its infancy, many people – including Starfleet officers – were hesitant to use the transporter despite the fact that it had been approved for bio-transport. According to Travis Mayweather, Captain Jonathan Archer himself even feared putting his dog through the transporter. (ENT: "Broken Bow") By 2155, the crew of Enterprise were getting more comfortable with the transporter and hence were not quite as reluctant to use the device. (ENT: "Demons")

Archer's fear to put his dog through the transporter would be realized in an alternate reality, when Montgomery Scott lost the animal in a subspace transport experiment.

When the Enterprise was about to launch to intercept V'Ger, the chief medical officer, Doctor Leonard McCoy, out of fear, refused to beam aboard the Enterprise, but Admiral James T. Kirk saw to it that he did. (Star Trek: The Motion Picture)

Ironically, Doctor McCoy may have had good reason to be afraid to step onto the transporter pad considering that not long before, the transporter had just killed science officer Sonak and another crewmember.

In 2364, after doing an inspection of the medical layout of the newly commissioned USS Enterprise-D, Leonard McCoy was still reluctant to use the transporter, preferring to use a shuttlecraft. (TNG: "Encounter at Farpoint")

Lt. Reginald Barclay suffered from transporter phobia when in 2369, he was faced with a difficult transport, the truth that he had never used the device came out. However, after a therapy session with Counselor Deanna Troi, he overcame his fear and was able to transport. (TNG: "Realm of Fear")

Other people who were not very fond of using transporters were Ensign Hoshi Sato, Dr. Leonard McCoy, and Dr. Katherine Pulaski. (ENT: "Vanishing Point"; Star Trek: The Motion Picture; TNG: "Unnatural Selection", "Shades of Gray")