Driver was originally drafted in 1981 by the Colorado Rockies, who subsequently transplanted to New Jersey. After leaving the University of Wisconsin a year early and after captaining a NCAA championship team, he played for Canada's national team for a season, playing in the 1984 Olympics in Sarajevo. Unfortunately, Canada finished just out of the medals in 4th place.
Soon after Driver turned pro, playing 12 seasons with the Devils and helped the team win its first-ever Stanley Cup in 1995. However, two months after tying for the club lead with a plus-13 rating in the postseason, Driver signed as an unrestricted free agent with the New York Rangers. The Devils felt he was near the end of his career and didn't want to match the contract the Rangers offered.
Driver played 3 seasons in New York, but played a lesser role. He helped to groom younger defensemen who would eventually fill his roster spot. In his final year, Driver played 75 games for the Rangers and had five goals and 15 assists.
Driver quietly established himself as one of the steadiest defensemen of his era. A smooth though not particularly fast skater, Driver was a good puck distributor with a good point shot, quarterbacking the Devils power play for many years. At 6' 0" and 185lbs he certainly wasn't the biggest blueliner, but he was smart positionally and dependable in his own zone.
Driver played in 922 career games, recording 96 goals and 390 assists for 670 points. He had 83 goals and 316 assists for 399 points with the Devils.