You've got a lot of other responses explaining lots of reasons why sports can be interesting, but I'll add my own.
IMO, if you think it's about watching strangers "kick a ball around," you're missing the point. It's about the
stories told through sports at least as much as the physical activity itself, and those stories generally transcend a single game.
Take baseball: a baseball season is a narrative as rich as movies and books, but watching one game between teams you don't know is like reading a page or two from the middle of a novel. You might get lucky and catch some enthralling action, but the real excitement comes from understanding that game in its context. The players on both teams each have their own stories, and the teams themselves have their own stories.
Take the drama between Marco Scutaro and Matt Holliday after the Holliday took out Scutaro in a dirty slide. On the surface, it's just a nasty play: http://mlb.mlb.com/video/play.jsp?content_id=25415817
But it happened in a major playoff series, which is exciting not just because "it's the playoffs", but because a grueling, 6-month 162-game series is on the line. (Picture what that means, don't just skim the numbers.) For the Giants, the slide looked eerily like the catastrophic injury last year that ended the season of a highly admired young rising star. (The significance of that injury comes from his role as a rookie the previous year in bringing the first World Series Championship to San Francisco, and the resulting high expectations for 2011 that were instantly crushed by that injury.) Scutaro himself was brought on mid-season to fill an important hole in the Giants offense, one which was supposed to be filled by Melky Cabrera, whom the fans grew to love dearly, but who betrayed fans by breaking league rules around performance enhancing drugs and getting suspended. There's lots more to this, but I'll leave it there.
As another example, take the last season game of 2011:
Day of: http://bats.blogs.nytimes.com/2011/09/28/leading-off-what-a-...
Day after: http://bats.blogs.nytimes.com/2011/09/29/leading-off-three-m...
So yeah, on the surface, it's just a bunch of guys hitting the ball around. But if you can put aside easy dismissal ("my local sports team is superior to your local sports team") for a minute and accept the conceit of the game, you may find the experience quite unique, in that the team element, the community of fellow fans, the rightness of both sides, and the fact that it's not scripted make it very different than most modern forms of storytelling, and it comes with its own insights on the human condition (see Pete Rose, the Black Sox scandal, or Jackie Robinson).
You might check out some of the Ken Burns documentary "Baseball" or Leonard Koppett's "The Thinking Fan's Guide to Baseball".