1947-1948: Totally different set-up to what we're used to. (It's apparently modeled after the ice hockey playoffs of the time.) In the first round, the second-place finishers of each division play against each other in a best-of-three series, while the third-place finishers do the same. In the second round, the winners of those series play a best-of-three series against each other, while the first-place finishers play against each other in a best-of-seven series. In the finals, the winners of the two second-round series play against each other in a best-of-seven series.
1949: A more familiar set-up, in which there are four best-of-three division semifinals, two best-of-three division finals, and a best-of-seven league championship series.
1950: This year, there are three divisions. One team (presumably the one with the best record) gets a bye between their division's finals and the league's finals, while the winners of the other two divisional finals duke it out in the third round to secure the other spot in the finals. Overall, the playoffs follow a 3-3-3-7 format.
1951-1953: Back to two divisions, but now with a 3-5-7 format.
1954: The playoffs begin with three-team round robins in each division. These are followed by two best-of-three division finals and a best-of-seven league finals.
1955-1957: Back to 3-5-7 format.
1958-1960: Now there is a 3-7-7 format.
1961-1967: Now there is a 5-7-7 format.
1968-1974: 7-7-7
1975-1983: 3-7-7-7
1984-2002: 5-7-7-7
2003-present: 7-7-7-7
Sources
Rosen, Charley (2008). The First Tip-Off: The Incredible Story of the Birth of the NBA. Mc-Graw Hill. pp. 211–212. ISBN0071487859.
Anderson, Corrie and Rob Reheuser, et al (2006). Sporting News Official 2006–2007 NBA Guide. Sporting News Books. ISBN0892048549.
Brown, Donald H. (2007). A Best of Basketball Story. AuthorHouse. pp. 4–5 ISBN1434341933. [3]