After having won Junior World Championships in both slalom and giant slalom, Raich made his debut in the Alpine Skiing World Cup in 1998, where he finished tenth. The following year, he earned his first victory in slalom. In 2002, he won two bronze medals at the Salt Lake City Winter Olympics.

In the 2005 Alpine Skiing World Championships, Raich won a total of five medals. He was also the first skier who won a Super-Combined. His sister, Carina Raich, is also a professional skier.