With their Game 3 victory, the Kings did something pretty damn special. No team in the long history of the NHL had ever gone ahead of their opponent 3 games to none in all four rounds of the Stanley Cup Finals as the Kings have now done against Vancouver, St. Louis, Phoenix, and New Jersey. It's been a playoffs full of firsts for the Kings (with hopefully one more to go), but this is one of the more impressive.
The NHL went to a four-round system in the 1974-75 season, but that year the preliminary round – which incidentally didn't feature all 12 teams who made the playoffs as the four division winners got byes into the second round* – was only a Best-of-Three while the remaining three rounds were all Best-of-Sevens, so no one could have gone 3-0 in all four rounds.
In the 1979-80 season, the NHL expanded the playoffs to include 16 of its 21 teams. The first round became a Best-of-Five. That system lasted until the 1985-86 season, in which time no team won all three games in the first round and then proceeded to lead the next three all 3-0.
In 1986-87, the league expanded the first round to be a Best-of-Seven, and even though the format has changed subsequently from a Divison-based playoff to a Conference-based playoff (in 1993-94), it has remained four Best-of-Seven series ever since. In that time, two teams, the 1995 Detroit Red Wings and the 2008 Pittsburgh Penguins, led the first 3 rounds 3-0, but both lost at least the first two games in the Stanley Cup Finals (Detroit got swept by New Jersey and Pittsburgh lost in six to Detroit). It's kind of odd that the last two teams to be so dominant through three rounds both bit the dust in the Finals. The 2012 Los Angeles Kings are the first to ever continue the streak into the Stanley Cup Finals, defeating New Jersey twice by 2-1 counts in overtime and then blowing them out in the third game, 4-0.
In case you're wondering whether it's been done in the NBA, the answer is no, but a few teams have come close since the 1984 season when the NBA first required teams to win 3 games to advance out of the first round. In back-to-back years, the Celtics and the Kings' co-tenants at the Great Western Forum, the Lakers, came the closest ever, within one victory in fact. The 1986 Celtics and 1987 Lakers went 11-1 in the first three rounds, each losing only their respective Game 4 of the second round, the Lakers to Golden State and the Celtics the Hawks, and then won the first two games of the NBA Finals. After moving to Staples Center the Lakers came pretty close again in the 2001 playoffs when they posted a perfect 11-0 mark through three rounds, but then lost Game 1 of the Final before winning the next 4 games. The Pistons led 3 rounds 3-0 in 1989, but dropped two of the first three to Chicago in the conference finals.
So the Kings have made not only NHL history, but North American sports history tonight.
*This was the season Kings fans talk about where they got screwed by the playoff system because the Kings had the 4th best record in the league but didn't win their division because they played with Montreal in the Norris while the Smythe features a bunch of terrible teams, so the Kings had to play the opening round Best-of-Three and after winning the first game at home, lost in Toronto, and then lost the decider back at the Forum.