I was curious too, so I went through hockey-reference.com to compile it. Here we go, the list of teams who have forced a game 7 after falling behind 3-0 (I highlighted in red the times the team that fell behind wound up winning the series):
1975 Semi-Finals. Philadelphia Flyers take a 3-0 lead on the New York Islanders; Flyers win series 4-3.
1975 Quarter-Finals. Pittsburgh Penguins take a 3-0 lead on the New York Islanders; Islanders win series 4-3.
1945 Stanley Cup Finals. Toronto Maple Leafs take a 3-0 lead on the Detroit Red Wings; Leafs win series 4-3.
1942 Stanley Cup Finals. Detroit Red Wings take a 3-0 lead on the Toronto Maple Leafs; Leafs win series 4-3.
1939 Semi-Finals. Boston Bruins take a 3-0 lead on the New York Rangers; Bruins win series 4-3. Interestingly enough, this was the first time the NHL implemented best of seven series since the NHL Finals in 1919, the only other time a best of seven had been used. Prior to 1939 the NHL had only used best of five and two game total-goal series (with the exception of 1919).
So teams falling down 3-0 have only forced a seventh game 5 times, and 2 of those times the team falling behind wound up winning the series. The Islanders almost did it twice in one year!
And in case anyone is interested, 1977 was the last time there were no game sevens in the playoffs.