Baseball? No. The "World Series" is just between American and one Canadian team with players mostly out of North America and the Caribbean.
American Football? No. Even though they say the Super Bowl is watched by people all over the world, and the US thinks it is THE whole world, it ain't.
Ice Hockey? No. Find me some outdoor ice rinks in Bangladesh or Indonesia and then get back to me.
Basketball? Yes. The sport has some serious traction around the world, but who really cares about it outside of March Madness, the NBA and international competition? There is a reason why the world's best players play in the US and not in Lithuania.
Rugby? Yes. Rugby is definitely a global sport. And once you're made into a Hollywood blockbuster, you know your sport has made it.
Hurling? I wish.
Then there's football (soccer), athletics (track), and cricket (cricket). I don't think anyone can argue that football is the most global sport. With pretty well every country in the world fielding a team that competes internationally, and high quality professional leagues scattered all over the world (yes, the best - and richest - concentrated in Europe), and the World Cup actually being a true World Cup, football is the sport.
Then we have cricket and athletics, and the two Jamaicans that dominate their respective sports, Gayle and Bolt.
Yes, it's only every 4 years that there's an Olympics or every two with a World Championship, but when the world watches, the entire world watches. And Bolt is indisputably the most recognized track athlete - and I would argue one of the top athletes irrespective of sport - in the world. He can play cricket too:
If you follow the IPL or cricket, or live in India, South Africa, Australia, the Caribbean, or England, Chris Gayle's name has become an adjective. His dominant and at-will batting has been described as a "Gayle Storm" or "Gayle Force". He's the most feared batsmen in T20 cricket, he's a match winner, and he's a fan favourite wherever he plays (except with the WICB, but that's another story).
Yes, Jamaicans are at the top of their game in the global sports arena.
Here's a Pepsi commercial for the football and cricket fans out there: