April 18, 1968: The Kings' first Game 7 was also in their first season in the NHL. The Kings faced the Minnesota North Stars in the first playoff series in franchise history and jumped out to a 2-0 series lead behind the goaltending of future Hall of Famer Terry Sawchuk. But the North Stars fought back, and a Game 6 overtime defeat in Minnesota set the stage for Game 7 in Los Angeles. Minnesota overwhelmed the one-time career shutout leader and the Kings, 9-4, to advance.
April 13, 1969: The Kings returned to the playoffs the following season and again faced a Game 7 in the first round. But in the first playoff Battle of California EVER, the Kings came out on top by beating the Oakland Seals 5-3 on the road in the deciding game. It was the first series win in franchise history, and though the St. Louis Blues would sweep the Kings in the semifinals, surely a Stanley Cup Finals berth wasn't far away! (It was.)
April 11, 1975: The third winner-take-all game in Kings' history was actually a Game 3. The NHL had undergone realignment with new expansion teams, and the playoffs now featured a best-of-3 opening round. LA had set a franchise record with 105 points (it still stands, by the way), and they were favored to defeat the Maple Leafs; however, they lost Game 2 in overtime in Toronto to set up a Game 3 the very next day in LA. Based on the Kings' history with back-to-back contests, you know what happened: Toronto won 2-1, eliminating the Kings.
April 25, 1976: The Kings rebounded in 1976 by winning their best-of-three opening series against the Atlanta Flames, then faced the favored Boston Bruins in the second round. The Kings faced elimination in Game 6 at the Forum, but Butch Goring was carried off the ice by his teammates after scoring one of the most famous goals in early Kings history to send the series to Game 7.
Unfortunately, Boston would win Game 7, 3-0.
April 9, 1977: For the third straight season, the Kings played a winner-take-all game in the playoffs, and they finally got a win after two consecutive defeats. LA took down the Atlanta Flames 4-2 in Game 3 of the opening round to advance, behind a hat trick by playoff hero Butch Goring. After the game, he said:
It was big men against little men and this time the little men won. We worked the whole season for the home ice advantage and fortunately we had it and it paid off. We worked hard and deserved the game. We played better than they did.
April 13, 1982: The Kings' first-round series against the heavily favored Edmonton Oilers is remembered for the Miracle on Manchester in Game 3, but many forget that the Oilers won the ensuing Game 4 to send the series to a decisive fifth game. The Kings made sure that the Miracle on Manchester would be more than just a footnote, taking down the Oilers 7-4 in Edmonton in Game 5 to advance to Round 2. There, they would lose to the Vancouver Canucks; the Kings would get revenge against Vancouver in 1991 and 1993 (and after a 2010 first-round defeat, they'd make up for it in 2012).
April 15, 1989: Former Oiler Wayne Gretzky and unexpected playoff hero Chris Kontos helped the Kings win the final Game 7 at the old Great Western Forum, defeating the Oilers 6-3. Kontos scored his eighth goal of the series, and Bernie Nicholls scored the game-winner on a 5-on-3 in the second period. It would be the final Game 7 in the Great Western Forum.
May 29, 1993: It's the most famous Game 7 in Los Angeles Kings history. After a controversial Game 6 overtime winner in LA sent the Campbell Conference Finals to Game 7, Wayne Gretzky put the team on his back and took the Kings to their first Stanley Cup Finals. Gretzky's hat trick helped LA defeat the Toronto Maple Leafs 5-4, setting the stage for a Stanley Cup Finals matchup with Montreal. The impending loss was devastating, but Gretzky's Game 7 performance still shines.
May 9, 2001: After the Kings took down the Detroit Red Wings in a memorable first-round series, LA faced Ray Bourque and the Colorado Avalanche in Round 2. The Kings fought back from 3-1 down to force Game 7, thanks to a Felix Potvin shutout in Game 5 and a Glen Murray overtime winner in Game 6. The seventh-seeded Kings finally succumbed to the Avs in the final game, losing 5-1 as Colorado would go on to win the Cup.
April 29, 2002: The underdog Kings once again pushed the Avalanche to the limit the following year, forcing a Game 7 in the first round thanks to wins in Games 5 and 6 behind Felix Potvin. And once again, the Avs dominated in Denver, sending the Kings home with a 4-0 win. The Kings would not return to the playoffs until 2010, and would not face another Game 7 until...
May 28, 2013: The first Game 7 in the history of the Staples Center. As Goring said back in 1977, the Kings had worked all year and won a crucial game at the end of the season to ensure that this deciding game of this series would be in Los Angeles. It paid off, as the Kings triumphed 2-1 over San Jose to move on to the Western Conference Finals. Justin Williams, the king of elimination games, scored both goals, while Jonathan Quick made a memorable glove stop on Joe Pavelski in the final minutes.
We've had to update this article a number of times in 2014, for obvious reasons.
April 30, 2014: The Kings complete the fourth comeback from a 3-0 deficit in NHL history, taking down the Sharks in Game 7 for the second straight season. Anze Kopitar scores a highlight-reel goal in the dying moments of the second period to put LA ahead for good, and the Kings advance to play the Anaheim Ducks in the first all-SoCal playoff series ever...
May 16, 2014: ... which also goes to a Game 7, naturally. The Kings once again demolish their in-state opponent, but this time, they do their work in the first half of the game by scoring the first five goals. The win sends them to the Western Conference Final for the third straight season. That's against the Chicago Blackhawks, and after going up 3-1 in the series, they lose two nailbiters to send the series to... Game 7.
June 1, 2014: The first June Game 7, and the most important Game 7 since 1993. This one is also the only one on the list which went to overtime, and as such, may be even more dramatic than 1993's. The result was the same, though; the Kings triumphed 5-4 to advance to the Stanley Cup Final. Gretzky was the hero of that 1993 Game 7, this time around, it was Alec Martinez, whose shot deflected off a Chicago defenseman and in for the winner.
(Thanks to the Kings website's History page for the help and the Goring quote. Feel free to explore!)