Of all of the baseball teams, it seems like the Cubs have the worst "curses". From the curse of the Billy Goat, 100 years without a World Series victory, the 1969 black cat incident and Steve Bartman, the Cubs will be known as a heavyweight in the history of sports curses.
October 6, 1945. Billy Sianis was turned away from the Cubs Tigers World Series game when he tried to bring a goat into the stadium. The story goes that Sianis was so mad that he set a curse on the Cubs, coincidently (or maybe not so coincidentally), the Cubs have not returned to the World Series since 1945. Here is a site that has a timeline for the Billy Goat curse and attempts to "reverse the curse".
Steve Bartman-October 14, 2003. Some Cub fans may need to turn their head for this one.
Game 6, National League divisional series, Cubs lead the Marlins 3 to 0 in this game and lead the series 3 games to 2. 5 outs from the World Series. Luis Castillo lifts a short fly ball into the left field corner of the stands. Moises Alou heads toward the wall, gets ready to time his leap to catch the ball that is heading towards the first row while a guy with glasses, headphones and a sweater is also going after the ball. Alou is unable to catch the ball, gesturing towards the fan who prevented him from catching the ball and slamming his hands down. From that point, the inning got way out of hand. Alex Gonzalez drops a routine double play ball and the Marlins get 8 runs in that 8th inning to help them take game 6, defeat Kerry Wood and the Cubs in game 7 on their way to their 2nd World Series championship. The ball was auctioned off and ultimately destroyed in a ceremony at Harry Carey's restaurant in Chicago, but alas the Cubs have not gotten that close to the World Series since 2003.
ESPN did a great job of replaying the incident. There are 10 You Tube clips of the "Bartman incident". I thought this part (#4) breaks down what happened very well which includes interviews of a few people in the stands near Steve Bartman.
I'm sure Ron Santo remembers a certain day in New York's Shae stadium when a black cat strolled past him on the on deck circle. The day was September 9, 1969. The Cubs lead of 1 1/2 games in the division was fading quickly and after this incident, the Cubs faded even further as they watched the "Miracle Mets" go on to win the 1969 World Series.