Steve Nash played on one Olympic basketball team: Canada’s men’s team at the 2000 Sydney Olympics.
Nash was Canada’s starting point guard and floor leader during the tournament. Canada advanced from the group stage and reached the quarterfinals, where it lost to France 68–63. The team finished seventh, according to Olympic statistical records, while Nash averaged 13.7 points, 3.3 rebounds, and 6.9 assists per game in the tournament.
Although Nash remained one of Canada’s most important basketball figures, he made only one Olympic appearance as a player. Canada failed to qualify for the 2004 Athens Olympics, and Nash’s later connection with the national program came through leadership and management roles rather than another Olympic playing appearance. He later served as general manager of the Canadian men’s national team.
The question asks how many Olympic basketball teams Nash played on, not how many international teams he represented overall. He played for Canada in other competitions, including FIBA events, but those appearances do not add another Olympic team to the answer.