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 25-year-old man sustained injuries to his head, arm and leg after falling from the spinning ride. Witnesses say the man, who removed his seat belt while the ride was cycling, may have been intoxicated. Source (in Spanish)
A 29-year-old woman suffered minor injuries when the kiddie carousel gondola detached and fell to the ground. She was riding with her 18-month old-son, who was not injured. Source (in German)
A park operative suffered leg injuries whilst working on the Dino Roller kiddie coaster. The operative was air lifted to hospital but his injuries were not life threatening. Source
A 13-year-old boy fell off a ride at the amusement park and was rushed to hospital, where he later died. Source
A 63-year-old park employee was killed when the new coaster train stuck the man whilst it was in operation. The employee had entered a restricted area. Source (in French)
A 32-year-old woman died after a falling from the 15-year-old Russian-made Pax Company wild mouse coaster. Source
A 56-year-old man died after being ejected from the alpine coaster sled into an embankment for unknown reasons. Investigators said the coaster ride and seat belts were determined to be in working order.
A 50-year-old man died and his 48-year-old wife was seriously hurt in the Daintree Rainforest when their zip line cable snapped and they fell more than 52 feet (16m) to the ground. The woman was hospitalized with suspected spinal, pelvic, shoulder and arm injuries. Source
A 21-year-old man suffered a broken pelvis and two broken wrists after falling 40 feet (12m) from a portable roller coaster he was assembling. Source
A 24-year-old mother of two died and her 20-year-old friend was hospitalized with traumatic brain injury after the women were ejected from their two-person chair approximately 33 feet (10m) to the ground. Source