Theme parks and roller coasters are statistically very, very, very safe. Out of the millions of people who ride the thousands of rides every year, there are only a small handful of incidents. You are statistically more likely to be involved in an accident driving to an amusement park than having one at a park. The rarity of accidents is one reason why the media report them, similar to plane crashes.
Every important element of a ride is inspected on a regular basis and every ride is tested every day without passengers before it opens. A ride might not open, or a safety system might activate, if there is an imperfection. For theme parks to operate, they must obtain insurance and one stipulation is their rides are frequently inspected and signed off by a strict Health & Safety governing body. Every theme park does what they can to prevent accidents because the negative press would be bad for business.
Having said all that, theme park accidents still happen…
A four-year-old girl died after falling 32 feet (10m) from the Sartori Rides magic carpet style ride. The child sat in her mother’s lap when the toddler slipped from her arms and fell from the moving ride to the pavement below. Source (in Spanish)
A duck boat carrying 31 people took on too much water and capsized during stormy weather, killing 17 people. Nine of the victims were family members, including an infant. Winds at the time were blowing as hard as 65 mph (104.5 km/h), according to the National Weather Service. Source (with video news report)
A 12-year-old girl was killed and 25 others injured when a Chinese knock-off Discovery rotating pendulum ride collapsed to the ground. The frisbee style ride was close to the highest point of completing a 360° swing of its mechanical arm, when the ride broke apart. The new Askari Amusement Park opened on June 14, 2018, but the ride was recently installed on a “trail basis” according to park management. Source
Four riders suffered minor injuries when a car on the ride broke off and crashed over the guardrails, after being hit by a second car. Source
Two people fell about 34 feet (10m) when the roller coaster derailed, sending six of the eight passengers to the hospital with minor injuries. The two thrown riders were in the front car, which was completely off the track and perpendicular to the ground, while four were in the partially-derailed middle car and two were in a rear car, which was still on the track. Source
Seven firefighters were injured in efforts to put out a massive fire at Germany’s largest amusement park. The fire at Europa Park completely destroyed the Pirates of Batavia boat ride as well large sections as the surrounding Dutch and Scandinavian-themed areas. Some 25,000 people had to be evacuated from the park, but none suffered any injuries. Source (includes video footage)
Three relatives between the ages of 12 and 19 were killed and two others injured when a Chinese built inverting coaster struck a maintenance crane arm that was moved too close to the track loop. The two crane operators, who were replacing light bulbs, and the ride op were detained in connection with the incident. Source
The train ride’s engine caught fire injuring two park employees and a guest. The park said no guests were on the ride, but one who received an injury from the incident was treated at the park’s medical center and released. The employees were taken to a hospital as a precaution. Source
A 22-year-old park worker was seriously injured when the SBF Visa kiddie spinning coaster ran over and pinned him under the ride. Emergency crews dismantled parts of the coaster train in order to free the worker, who was transported to hospital with leg wounds. Source (with video news report)
An 11-year-old girl fell out of a boat on the river rapids ride and suffered serious injuries. She was air-lifted to hospital, where she passed away shortly after arrival. Source