A man suffered a broken arm after extending it outside the Alpine Coaster car during the ride and was transported to a local hospital. Source
Accidents
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…
Gatlinburg Mountain Coaster, Tennessee, USA
A 44-year-old woman was thrown from the Alpine Coaster car suffering fractures of both wrists, a kneecap, head trauma, and possible broken ribs. Source
Raging River, Adventureland, Iowa, USA
A 68-year-old employee died when he fell on the ride’s conveyor belt, fracturing his skull and suffering a major brain injury. Source
Tsunami, M&Ds Scotland’s Theme Park, UK
Nine children and two adults were hospitalised after all five carriages on the Pinfari-manufactured coaster came off the tracks, plunging roughly 20 feet (6m) to the ground and hitting a child’s car ride, before coming to a rest upside down, leaving riders trapped. Source

Zippin Pippin, Bay Beach, Wisconsin, USA
One rider and two workers were injured when an occupied train failed to stop properly, hitting an empty train in the loading area, which in turn hit the workers. Source (with video report)
Disco Dancer, Kishkinta Theme Park, Chennai, India
A 25-year-old man was killed and 10 others injured when employees were forced to test a Disk-O knockoff ride that came off the track and crashed to the ground. Source
King’s Crown, Cinco de Mayo Carnival, Nebraska, USA
An 11-year-old girl lost her scalp and fractured her skull on the spinning carnival ride when her hair got sucked into the ride’s machinery. Source (with video report)
Boomerang, Six Flags St. Louis, Missouri, USA
Four people received minor injuries after the coaster abruptly stopped mid-ride, with two cars de-railing off the track. Source (with video report)
Flying Chairs, Mundo Divertido, Tijuana, Mexico
The central support structure of the ride gave way and the swings people were sitting in flew off the ride, injuring seven children and five adults, including a 3-year-old and a pregnant woman. Source

Phantom Manor, Disneyland Paris, France
A 45-year-old technician was found dead in the park’s Haunted House after he was believed to have been electrocuted. Source