Ginther was born in Hollywood, California. His family moved briefly to Ohio for his father's work before returning to California and settling in Santa Monica — the same town as future Formula One world champion Phil Hill. It was through Hill, a friend of Ginther's older brother George, that he first became involved in racing. After leaving school in 1948 Ginther worked for Douglas Aircraft, and in his spare time helped Hill maintain and race his collection of old cars and hot rods.
He made his race debut at Pebble Beach in 1951 in a Ford-engined MG T-type. His career was then interrupted by two years of national service during the Korean War, where he gained valuable experience in aircraft and engine mechanics. After returning from service, he joined Hill as a riding mechanic in a Ferrari entered in the 1953 Carrera Panamericana — a race the pair did not finish — before returning in 1954 to take second place behind the works Ferrari of Umberto Maglioli.
Through the mid-1950s Ginther raced on the West Coast, initially in an Austin-Healey and then in Porsche machinery for dealer John von Neumann. When von Neumann took on a Ferrari franchise in 1956, Ginther's circle expanded: his reputation on the West Coast caught the attention of Luigi Chinetti, Ferrari's North American importer and NART team boss, who first used him in 1957. By the end of the 1950s Ginther had won the Pacific Coast Sports Car Championship.
Ginther made his Formula One debut at the 1960 Monaco Grand Prix driving for Ferrari. At the Italian Grand Prix that September he finished second to Phil Hill, having led for the first 25 laps. In 1961, as the third Ferrari driver behind Wolfgang von Trips and Hill, he was a key part of the dominant Scuderia operation. He finished a close second to Stirling Moss at the 1961 Monaco Grand Prix, just 3.6 seconds behind after 100 laps, and was regularly competitive throughout the season.
The tragedy of the 1961 Italian Grand Prix at Monza — where von Trips died in a crash that also killed fifteen spectators — ended the season on a deeply sombre note. Ferrari withdrew from all competition until January 1962 as a mark of respect.
Ginther moved to BRM in 1962, partnering Graham Hill. His 1963 season produced his best championship result: equal-third in the World Drivers' Championship alongside Graham Hill, though Ginther had actually scored more points than his British teammate over the season. The championship counted only a driver's six best finishes, however, which favoured Hill's tally over Ginther's consistency.
Ginther's reputation within the paddock was built on precision, reliability, and an exceptional ability to develop and provide technical feedback on racing cars — qualities that attracted the attention of Honda when the Japanese manufacturer entered Formula One.
Honda recruited Ginther as their works Formula One driver for 1965. The season's final race, the Mexican Grand Prix, provided a historic result: Ginther won the race, giving Honda its first Formula One victory and simultaneously recording the first win on Goodyear tyres in the championship. He averaged 151.7 kilometres per hour over the 65-lap event at the Mexico City circuit, eclipsing Dan Gurney's previous course record.
He continued with Honda into 1966, leading the Italian Grand Prix before crashing into a barrier and breaking his collarbone. He then signed with Dan Gurney's Eagle team for 1967. The 1967 Monaco Grand Prix proved to be Ginther's final Formula One entry; he failed to qualify. He retired from racing that year, in part prompted by the recent fiery death of his close friend Lorenzo Bandini, and in part by a frightening incident in practice for the Indianapolis 500 when a broken fuel line sprayed a fuel mixture over his back.
During the filming of the 1966 feature film Grand Prix, Ginther participated both as a technical racing advisor and in an uncredited acting role, playing a driver in the Japanese-funded "Yamura" team. After retiring from racing he managed a Porsche 911S entry at the 1971 24 Hours of Le Mans.
Ginther died of a heart attack on 20 September 1989 while on vacation with his family in Touzac, near Bordeaux, France. He was 59. He was inducted into the Motorsports Hall of Fame of America in 2008, and a biography — Richie Ginther: Motor Racing's Free Thinker by Richard Jenkins — was published in 2020 to mark what would have been his 90th birthday, winning the RAC Motoring Book of the Year Award.