Born in Milan, Paletti was the son of Gianna and Arietto Paletti, a Milanese entrepreneur who had built his fortune as a real estate developer and was the importer for Pioneer audio equipment in Italy. Paletti's early sporting interests were broad; he was Italian junior karate champion at thirteen and was in contention for a place on the Italian national alpine skiing youth team.
Paletti entered nine races in Formula Super Ford in 1978, leading for 18 laps in his inaugural race. Although he did not win during the first season, he took two second places and finished third in the overall championship. During the end of his first season, he also made his Formula 3 debut in the Italian Championship with a March-Toyota. In 1979, Paletti entered a full F3 championship season, but his best placings were two fifth-place finishes. Later the same year, he competed in a few Formula 2 races for the first time with the team run by Mike Earle, finishing eighth at Misano.
For the 1981 European F2 championship season, Earle started the Onyx team. Paletti tested extensively during the winter, and the effort paid off during the opening rounds. He qualified 10th at Silverstone before finishing second behind Mike Thackwell. He retired in the second round at Hockenheim but set the fastest lap of the race, and finished third at Thruxton behind Roberto Guerrero. At that point, he was joint second in the championship with Stefan Johansson, trailing Thackwell by three points. However, his results declined, and he finished tenth in the championship.
Paletti joined the uncompetitive Osella team in 1982. He admitted that Formula One struck him with a little bit of fear, but his sponsor, Pioneer, wanted him to move up and Paletti did not want to miss his opportunity. His teammate was the experienced Frenchman Jean-Pierre Jarier. Paletti traveled with a personal medical adviser who monitored his blood pressure and heartbeat with small sensors attached to his body during testing and practice sessions. His diet was constantly adapted to the results, a professional approach few Formula One drivers took seriously at the time.
Paletti failed to qualify for the South African, Brazilian, and US GP West Grands Prix. At Imola, amidst a war between FISA and FOCA, Paletti started from the back of the grid. However, his Osella failed to fire up for the warm-up lap, and he was 49 seconds behind the field by the time he crossed the starting line. He retired after seven laps due to a suspension failure. He failed to prequalify at Zolder and Monaco. In Detroit, he qualified right behind Jarier, but a series of mechanical issues and a crash by Jarier resulted in Jarier taking the only available car, leaving Paletti as a spectator.
Paletti qualified for the Canadian Grand Prix on Sunday 13 June 1982, the first time he would start successfully in a full line-up. At the start, the lights took an unusually long time to turn to green. During this time, pole-sitter Didier Pironi stalled the engine of his Ferrari. Pironi lifted his hand to signal the problem just as the lights switched to green. Raul Boesel "just clipped the back left of the Ferrari," spinning his March into the path of Eliseo Salazar and Jochen Mass. Paletti could not react in time and slammed into the rear of the stranded Ferrari at 180 km/h (110 mph), catapulting it into the path of Geoff Lees.
Due to the force of the severe impact, Paletti sustained heavy chest injuries and was lying unconscious in his car, wedged against the steering wheel. Sid Watkins, the FIA's head doctor, was on the scene to stabilise and assist Paletti. As Watkins climbed over the wreckage of the Osella, the petrol from the fuel tank ignited, enveloping the car in a wall of fire. When the fire was finally put out, the injured Paletti was without a pulse. "It took the rescue workers 25 minutes to cut him out safely from his wrecked car, as the sparks caused by the cutting equipment threatened to re-ignite the petrol on the track." He was flown by a medical helicopter to the Royal Victoria Hospital, where he died soon after arriving. Paletti suffered a torn aorta as well as fractures to both legs. According to track doctor Jacques Bouchard, his pupils were already dilated when medical personnel arrived and the extended extraction time made no difference to his chances of survival.
Paletti was the second Formula One driver to die during the 1982 season, following Gilles Villeneuve. He was the last Formula One driver to die in a race until the 1994 San Marino Grand Prix, which saw the deaths of Roland Ratzenberger and Ayrton Senna. In 1986, Elio de Angelis was killed during testing, but the test was not part of a Grand Prix.
In tribute to Paletti, the racetrack at Varano de' Melegari is now called the Autodromo Riccardo Paletti. There is also a side altar in the Church of Santa Maria al Carrobiolo, Monza dedicated to his memory, and he is buried at the Cimitero Maggiore di Milano. In July 1982, the Italy national football team dedicated their World Cup victory to Villeneuve and Paletti, holding a banner that read "Villeneuve, Paletti... Corriamo insieme, il terzo titolo è nostro!" (Villeneuve, Paletti... We speed together, the third title is ours!).