Sad, but true story of this franchise.
In 1986 this team was one out (one retired batter) from going to the World Series. They were in the American League finals (baseball's version of the semifinals) and led the Boston Red Sox three games to one in the best 4 of 7 series. They were ahead by a run in this particular game.
It was the top of the ninth inning (Boston's last chance to score) and they had two outs. The California pitcher, Donnie Moore came into the game after the Red Sox had pulled within 5-4 and had two strikes on the next hitter, Dave Henderson. The home crowd (the game was played in Anaheim) rose as one and prepared to run on the field to celebrate.
Everything's cool, right? Wrong.
Henderson hit a home run. Since there was a runner on first as well, this put Boston ahead 6-5. California tied the score in the bottom of the inning, but Boston would win the game in extra innings.
Boston would win the series the next week by winning two straight games at home (in Boston). The Angels didn't come that close to the World Series again until 2002 (when they won it).
Moore was never the same after Henderson's home run. He played until 1989, and the winter after that season, he shot and killed himself.