Growing up in New England, racing wasn't the first thing on Craven's mind. But at the age of 15, he began racing at Unity Raceway, winning twice as well as the Rookie of the Year award. The next year, he won 12 feature events and the track championship. After that, he began running in the Canadian-American tour, where he had rampant success. In 1986, he made his NASCAR debut at Oxford Plains Speedway in his own number 12, finishing 25th after suffering engine failure. Four years later, he began running the Busch North Series, winning the Rookie of the Year award. In 1991, he was named the champion in that series. In addition, he made his Winston Cup debut at Rockingham, starting and finishing 34th, as well as winning two races in the Busch Series running a limited schedule. He moved to the Busch Series full-time in 1992, and once again was named Rookie of the Year. In 1993 & 1994, he finished runner-up to Steve Grissom and David Green, respectively, in the championship standings. This performance caught the eye of several Winston Cup team owners.
In 1995, Craven teamed up with Larry Hedrick Motorsports and Kodiak to run for Winston Cup Rookie of the Year. Craven qualified for all 31 races, finished in the top-ten four times, and was able to defeat Robert Pressley for the top rookie award. For his efforts, he was rewarded with a partial ownership share in the team. His performance improved even more in 1996, winning two poles and nailing down a 20th place finish in points. At the end of the year, he was given the opportunity of a lifetime, to drive the number 25 for the premier Hendrick Motorsports team. Craven obviously signed immediately, and at first, the future seemed bright, as Craven finished in the top-five in the first two races, but it was soon disrupted. While practicing for the inaugural Interstate Batteries 500, Craven crashed hard into the wall. He missed two races due to a concussion suffered from the wreck. It didn't seem to affect him at first, as he won the Winston Open and finished a career-best 19th in points. Hopes were high in 1998, but after the season started, the side effects of the concussion began to creep out, and Craven was forced onto the sidelines until he got better. He returned at his home track at New Hampshire International Speedway later that year, and to the surprise of everyone, won the pole. After four races however, it was obvious he had rushed his return and left Hendrick permanately, and didn't return until the final three races of the season, filling in for Ernie Irvan at MB2 Motorsports.
For 1999, Craven decided to sign up to drive the number 58 Ford Taurus for SBIII Motorsports, a brand new team in NASCAR. The result was disappointing, as Craven did not finish any better than 19th while he drove the car. After he failed to qualify for the Coca-Cola 600, he was replaced by Loy Allen Jr. in the car, and he was once again unemployed. Not too long after that, he signed up with another new team, Midwest Transit Racing who had struggled with rookie Dan Pardus at the wheel. The combination had satisfactory results, and the combo immediately decided to sign up again for 2000. Unfortunately, thanks to DNQ's and a tight budget, Craven didn't even run half the races that year. By the end of the season, he was already talking to Cal Wells, owner of PPI Motorsports. In January the next year, it was announced he would replace Scott Pruett in PPI's number 32 Tide Ford. This time, success was more evident, as Craven shockingly won the pole at the summer race at Michigan International Speedway. And at the Old Dominion 500 at Martinsville Speedway, Craven held off Dale Jarrett in the closing laps for his first career Winston Cup win. 2002 was even better, as he won two poles, finished in the top-ten nine times, and finished a career-best 15th in points. Craven would forever become a part of NASCAR history in 2003, when at the spring race at Darlington Speedway, he battled Kurt Busch for the win, defeating him by a mere fraction of a second in what is considered by many to be the most exciting finish in NASCAR history. Unfortunately, Craven couldn't carry that milestone over for the rest of the year, and dropped twelve spots in points. After he didn't post a single top-ten finish three-quarters of the way through the 2004 season, he was replaced by Bobby Hamilton Jr., and only returned to run at his home track at New Hampshire. Still Craven was able to land another job, just in another series. He signed to drive the number 99 Superchips Ford for Roush Racing in the Craftsman Truck Series. Despite a win at Martinsville Speedway and a fourteenth place finish in points, he and Roush parted ways when the season came to a close.