Born in South Africa under apartheid, Plaatjes won two national titles at the marathon and two at cross country . He ran a personal best marathon of 2:08:58 in 1985 in Port Elizabeth, but was unable to compete outside South Africa, barred from the 1984 and 1988 Olympic Games due to the international boycott of South Africa. He sought political asylum in the United States in 1988, saying "I didn't want my daughter to grow up in a country where she felt inferior."
In 1993, Plaatjes finished 6th in the Boston Marathon, qualifying for the U.S. team at the World Championships. On 24 July 1993, Plaatjes became a citizen of the U.S., just three weeks before the World Championships. Stuttgart was to be the greatest success of his career. The race had been led by Luketz Swartbooi from Namibia for a very long time. At 40 km, Swartbooi still looked like the likely winner. But the Namibian slowed down in the very final stages and was overtaken by Plaatjes three minutes before he reached the finish line, in a time of 2:13:57. Plaatjes became the first American to win a gold medal in a long-distance event at World Championships.
Plaatjes has made his home in Boulder, Colorado, where he has a hand in several local businesses and coaches a local running club.