How far back in history do you want to go? The Native Americans in Canada played a game very much like Lacrosse and the Mayan or Inca culture played a form of soccer. Both of these games often used a human skull for a ball.
If you just mean since the settlement by Caucasians, some Pilgrim probably said "last one to that rock is a rotten egg" and started a footrace. Target shooting would probably have been a very early competitive sport. Hunting, at that time, would have been an occupation, not a sport.
If you just mean professional sports, bare-knuckle boxing may be the oldest, but it was not organized. The "champion" would travel from town to town in the old west and challenge the local tough guys, offering prize money to anyone who could beat him, but collecting enough in admission fees that he didn't go away without some profit even if he lost.
Lacrosse is the oldest American sport they played the game for days at a time sometimes even though the sport is not played the same the variation is different it was played as a sport even though it wasn't professional it was a sport that was played before there was horses or bulls in America not sure about fencing but don't think native Americans had fencing swords.
wrestling
Baseball is the oldest of the major American teamsports
basketball
Midget Tossing
Lacrosse (oldest American Sport), Hockey (not really American, though)
La Cross is not a cross of any sport its the oldest North American sport ...
Basketball is most popular and oldest surviving sport.
before written history. oldest field sport know to man
I know that it is running. You only have to read Greek history to know it.
I think polo is an oldest animal sport
I would say that the oldest team in the history of modern sport, anyways, would have to be the (now) Chicago Cubs. They formed in 1876 as part of the National League.
Mayan mask?