There has not been a single team in the NBA going 12-0 into the finals. This is also due to the first round being a best of 5 game series until the 2003 playoffs. The 2000-2001 Los Angeles Lakers' actually went 11-0 into the finals before losing game 1 to the Philadelphia 76'ers. They won game 2,3,4 and 5 to win the NBA championship with a playoff record of 15-1. The best in history (so far).
The 16-17 Golden State Warriors are the first team to ever reach the NBA Finals with a 12-0 record.
In the NHL the 1991–92 Chicago Blackhawks, 1991–92 Pittsburgh Penguins, and 1992–93 Montreal Canadiens had eleven game win streaks in the playoffs, but those streaks did not begin until later into the playoffs, such that each team lost opening round games.