The Detroit Pistons famously did it against the Orlando Magic in (I believe) 2003.
Tracy McGrady commented that it felt great to finally reach the 2nd round, though the Magic only led 3-1 (JINX!).
Tayshaun Prince cemented his reputation as one of the best SF defenders in the league by slowing McGrady for the next 3 games and helping to win the series.
No teams in the NBA have ever come back from a 3-o series deficit in any NBA 7 game series including the Finals.
Toronto Maples Leafs vs Detroit (1942) New York Islanders vs. Pittsburgh (1975) Philadelphia Flyers vs Boston (2010) L.A. Kings vs. San Jose (2014)
Looks like the Heat will.
The 2001 New York Yankees
Five teams have done it in a seven-game World Series: 1925 Pirates 1958 Yankees 1968 Tigers 1979 Pirates 1985 Royals The Boston (AL) team also won the Series in 1903 after being down 3-1, but that was a nine-game series.
Which NBA teams have come back after being 3-0 in a playoff series
Sharks
miami heat 2006 vs dallas
No one has completed this feat in NBA history yet
You can add one more to that list however many it is, because the Miami Heat are about to do it
Most of the teams who have successfully rallied from a 3-1 hole (six of the eight) enjoyed homecourt advantage.
There are actually only 7 teams in the NBA who rallied from 3-1 to win a playoff series. They are the Boston Celtics (1968), Los Angeles Lakers (1970), Washington Bullets (1979), Boston Celtics (1981), Houston Rockets (1995), Miami Heat (1997), Detroit Pistons (2003) and the Phoenix Suns (2006). So Mathematically only 23.33% of all NBA teams won an NBA playoff trailing from 3-1.
There were no teams ever came back from 3-0 deficit. There were some who forced a game 7 though. However, there were 7 teams to win a playoff series from 3-1 deficit.
The Boston celtics in Chicago in 2009 and nuggets lakers 2009 when lakers stormed back into a 4-2 series win
No teams in the NBA have ever come back from a 3-o series deficit in any NBA 7 game series including the Finals.
Toronto Maples Leafs vs Detroit (1942) New York Islanders vs. Pittsburgh (1975) Philadelphia Flyers vs Boston (2010) L.A. Kings vs. San Jose (2014)
Looks like the Heat will.