Vogler emerged from the national midget ranks, winning the National Alliance of Midget Auto Racing (NAMAR) midget championship in 1973. His ascent through USAC was swift and commanding. He claimed USAC National Midget Series championships in 1978, 1980, 1983, 1986, and 1988 — a total of five national midget titles. He also captured USAC National Sprint Car Series championships in 1980 and 1989.
In 1980, Vogler became the first driver ever to win both the USAC Sprint Car and Midget championships in the same season, a feat that cemented his status as the most complete oval short-track racer of his generation. His dominance at regional tracks was equally impressive: he won the midget car track championships at the Indianapolis Speedrome in 1984 and 1985, and was a recurring winner at venues such as Salem Speedway and Winchester Speedway.
Vogler's record in prestigious invitational events was extraordinary. He won the Hut Hundred eight times — a USAC midget event held at Terre Haute Action Track — and the 4-Crown Nationals midget car event four times. He won the Copper Classic twice, the Hoosierdome Invitational twice, the WWRA Florida Winter Nationals in 1983, and the Night Before the 500 once. In 1987, he won the inaugural Chili Bowl Midget Nationals, a race that would go on to become one of the most celebrated events in American open-wheel short-track racing.
Vogler made his Indianapolis 500 debut in 1985, driving the No. 60 Patrick Racing entry sponsored by Jonathan Byrd to a 23rd-place finish. He made consecutive starts at Indianapolis from 1985 through 1990, maintaining a long professional relationship with sponsor Jonathan Byrd throughout his IndyCar tenure.
His best Indianapolis 500 finish was eighth place in 1989. In 1988, Vogler was running laps down in the race when he gestured to allow former Formula 1 champion Emerson Fittipaldi past him. USAC officials, however, did not observe the waive and penalized Fittipaldi two laps. Vogler went to USAC to testify on Fittipaldi's behalf, calling the penalty unjust. The penalty was overturned the following morning, and Fittipaldi was credited with the runner-up position.
Vogler's 134 wins in USAC national events — 95 in midgets, 35 in sprints, and four in Silver Crown — is second only to A.J. Foyt's 169. His total of 170 USAC wins does not account for the more than 200 additional victories he accumulated in non-USAC outlaw midget races, making his overall career win total well above 370 feature victories. He also made one NASCAR Busch Series start, finishing seventeenth at the North Carolina Speedway in Rockingham in 1988, and was lined up to make his NASCAR Winston Cup debut at Pocono Raceway.
On July 21, 1990 — five days before his fortieth birthday — Vogler was competing in the nationally broadcast ESPN Thunder Joe James / Pat O'Connor Memorial sprint car event at Salem Speedway in Indiana. He was leading the race with just over a lap remaining when his car was involved in a crash. Vogler's helmet came off in the accident, and he suffered severe head injuries that proved fatal instantly.
Due to USAC red-flag rules reverting to the previous completed lap, Vogler was posthumously declared the winner of the race — his 170th USAC national win. He had been scheduled to attempt his first Winston Cup start the very next day at Pocono Raceway, and had been preparing for a planned full-season Winston Cup campaign for U.S. Racing; that seat was subsequently filled by Ted Musgrave.
Vogler's mother Eleanor established a college scholarship fund for Indiana students in his memory, with support from USAC officials and sponsor Valvoline. The fund's inaugural major fundraiser was a Daytona 500 viewing party in Indianapolis, and the fund has continued with annual events into the 2000s, including a 2008 gathering at Indianapolis Motor Speedway coinciding with a race won by 1996 scholarship recipient Ryan Newman.
In April 1991, Winchester Speedway inaugurated the annual Rich Vogler Classic sprint car race, held as the season-opening event each year. The Indianapolis Speedrome also hosts a Team Vogler Classic in his honor. Vogler was inducted into the National Midget Auto Racing Hall of Fame in 1986, the National Sprint Car Hall of Fame in 1992 in the first eligible year, and the Motorsports Hall of Fame of America in 2010.