Baseball - End of the regular season, and playoff time! With three division winners and two wild cards in each league, the end of the regular season can often be almost as exciting as the playoffs themselves. There's the one-game wild-card playoffs, of course, and then the division and league series. Even the World Series might be played entirely in October...though I hope not, since games 5-7 are scheduled in early November. Games 6 and 7 are the best part!
Football - The NFL regular season is underway, and every weekend has college football action. The biggest regular-season games are still a month or two away, but since football has a small number of total games to play, even these early season contests are important and dramatic. Especially when highly ranked college teams meet early on.
Hockey - The NHL regular season begins! With a fight, this year, but eventually they actually play the game. It's a long season, so the other sports tend to overshadow the opening weeks, but it's there.
Basketball - Most of the month is pre-season for the NBA, but the regular season starts just before Halloween. The WNBA finals are going on, too, though that league still mostly flies under the radar.
October isn't quite as crowded outside the USA, but there's still action. There's the Champions League, and this year the Rugby World Cup is going on. In any other month, I'd be following the rugby action over in England with more attention, but it's hard to focus with everything else going on!
Fall is a great time to be a sports fan. As long as you don't try to watch it all, anyway!