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 13-year-old girl injured her foot after it was crushed by the air show ride’s lowering platform, resulting in the loss of one of her toes. The incident occurred as she was about to board the rotating pendulum ride. Source
A 31-year-old male employee suffered serious injuries when he attempted to jump from one side of the Fabbri rotating pendulum booster ride to the other and was struck by the gondola. Source (in Dutch)
An 8-year-old boy was injured after being thrown from the Himalaya style spinning ride into a 50-year-old woman, who received minor injuries. The boy suffered head trauma, back pain and bruising to his arms and legs. Source
A 20-year-old male worker suffered severe head trauma after being struck by the gondola of the Fabbri Booster Maxx rotating pendulum ride. First responders rushed the man to a local hospital, where he remains in a coma. Source (in French)
Two children aged 12 and 9 were slightly injured, while their 47-year-old mother and their 74-year-old grandmother suffered more serious injuries when the former Diamond Amusement Rides traveling roller coaster suffered an axle break, causing a derailment. The four family members were transported to a hospital for treatment. Source (in French)
An 18-year-old man was ejected from the Musik Express/Himalaya style ride at the Canadian National Exhibition, suffering serious but non-life-threatening injuries. It appeared that the young man tried to stand up on the ride while it was moving at high speed. Source
A 17-year-old boy and a 19-year-old woman dropped some 180 feet (60 m) from the Sky Coaster during high winds and collided with nearby objects. Paramedics took both victims to a local hospital for treatment, where doctors declared the boy dead. Source (in French)
A child suffered injuries on the spinning kiddie attraction after exiting the ride before it came to a complete stop and was transported to a local hospital for evaluation. Source
A woman working at the amusement park sustained a minor concussion after being hit by the Intamin Zac Spin roller coaster. Source (in Swedish)
A 45-year-old male employee of the fair died while conducting routine maintenance on the spinning attraction. Source