Berg began racing karts in Alberta, Canada in 1978, moving into Canadian Formula Ford in 1980 . The following year he finished second to Scott Goodyear. He then moved up to Formula Atlantic in 1982, and won the rookie of the year award.
In late 1982 he travelled to Australia to race in the Formula Pacific Tasman Championship for ex-racer Graeme Lawrence in a Ralt, winning the Lady Wigram Trophy and the title. As a result he was offered a drive with Neil Trundle Racing in the British Formula 3 Championship in 1983.
After a poor start to his campaign he switched In the middle of the season, to Eddie Jordan Racing, but could do little else but pick up the scraps of the battle between Ayrton Senna and Martin Brundle. Allen won a race at Silverstone and ended fifth in the championship behind Senna, Brundle, Davy Jones and Calvin Fish. The following year he consistentley finished second behind Johnny Dumfries, ending the year second in the series. It was not enough and in 1985 Berg returned to Canada to try to find money, racing in Mexico to keep the wolf from the door.
In 1986 he found backing from the Swiss company Landis & Gyr which gave him the chance to buy a drive with Osella in F1 after Christian Danner had moved over to Arrows. He qualified for nine races despite the difficult car, but it was not enough and Berg once again returned to Canada.
He only raced occasionally between 1987 and 1989 in sportscar events, he also tested for the Jaguar IMSA team and raced in TransAm.
In 1990 he raced at Le Mans with Richard Lloyd Racing before heading to Japan to race sportscars there.
In 1991 he returned to Europe racing in the German touring car championship with a privately entered BMW with Tic-Tac sponsorship.
After a poor season, Berg returned to Canada but deceided to go to Mexico the following year. Marlboro were offering big sponsorship in the local F2 championship. He was third in 1992 and won the title in 1993, while also racing in local sportscar events as well.
He continued racing in Mexico, winning the Formula 3 title in 1997 and the Panamerican Indy Lights title in 2001.
In 2002 he went into team management in the Toyota Atlantic series in the US and Canada.
