Transporter use carries an inherent risk, since transporters break down and recomposite molecular structures. Transporter phobia is a fear of using the devices.
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") However, by 2155, the crew of the NX-01 Enterprise were getting more comfortable with the transporter and hence were no quite as reluctant to use the device. (ENT: "Demons")
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 meeting 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 transporters were Dr. Leonard McCoy and Dr. Katherine Pulaski.