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 29-year-old employee, who was inspecting the S&S roller coaster, got caught between a stopped vehicle and rail, and later died at a local hospital. The employee was part of an 11-man team inspecting the ride, which was closed for the day and not in operation at the time of the incident. Source (in Japanese)
Although it’s not an accident, a 14-year-old boy died after suffering a heart attack during a school trip to the park. The incident occurred when the student started feeling uneasy, sat on a bench, and collapsed on the ground. Source
A 13-year-old girl was injured after being ejected from the Chance Rides spinning Trabant-style attraction. Source
A couple suffered minor injuries when they were thrown out of the breakdance-style ride after the passenger gondola collapsed due to defective bearings in one of the ride’s arms. Source (in Portuguese)
A 17-year-old employee died when the go-kart he was driving collided with an industrial forklift, which another park employee was also operating. Source
A 17-year-old boy died after he disembarked the Morgan hyper coaster when he suddenly reported feeling unwell and collapsed. Paramedics transported the boy to a local hospital, where he was pronounced dead. An autopsy revealed he had sustained cerebral and pulmonary edema. Source (in Spanish)
A 14-year-old girl sustained several fractured vertebrae when the local fair’s drop tower malfunctioned and dropped to the ground. Source (in Spanish)
Two women were taken to hospital with minor injuries after the 180-foot (55 m) tall Star Flyer failed and crashed to the ground while in operation. Another 11 riders were assessed by paramedics and discharged at the scene. Source
A young boy was hurt and transported to hospital for observation after the Ferris Wheel he was riding at the Christmas Fair got caught as it cycled. Source (in German)
A motorcyclist broke his collarbone when he lost control of the motorbike and crashed on a wet road. Source (in Portugese)