What is the oldest continuously held sporting event in the USA?

*** THIS QUESTION IS A FAQ - this top post will be used to provide the best info from below ***

There are a TON of events that claim to be "the longest running". Fortunately we can just compare dates.

Jousting Competition, Natural Chimneys, (Since at least 1840)

There’s not a ton of great documentation floating around out there to corroborate the oral tradition, though. The tale of the inaugural 1821 joust has been rewritten time and again in local newspapers and other accounts, and a 1941 article in the Maryland Historical Magazine mentions the yearly tournament at Natural Chimneys as one of the best-known jousts in the South. Nevertheless, the article identifies an 1840 joust outside of Baltimore as the first to definitively occur in the United States.

http://modernfarmer.com/2014/10/faded-glory-americas-allegedly-oldest-sporting-event/

America's Cup, 1851 -- except, it's not always been raced in the USA.
https://en.wikipedia.org/wiki/America%27s_Cup#1851:_America_wins_the_Cup


Intercollegiate boat races (rowing) first held between Harvard and Yale in 1852. NOTE: First contested in 1852, annually since 1859 except during major wars fought by the United States.

Kentucky Derby (1875) -- lots of claims that this is the oldest, but it doesn't appear to be unless you disqualify those listed above.

https://en.wikipedia.org/wiki/Harvard-Yale_Regatta

I don't know if this is what you want, but I found this info:
The Westminster Kennel Club Dog Show is the second oldest continuous sporting event in the U.S. What is the oldest? The Kentucky Derby, a mere twenty months older, is the only event which beats out the Dog Show as the oldest continuous sporting event in America. The Westminster Kennel Club Dog Show been held faithfully each year for the past 123 years, despite power shortages, hazardous snow storms, national depressions, and World Wars.

You are overlooking the America's Cup. Competition was begun in 1851, and for 132 years, the American team successfully defended the cup.

the annual US V Canada cricket match was inaugurated in 1844 (canada won incidentally) - some 32 years before the first test match between England and Australia.

The Kentucky Derby claims to be the oldest continuously held sporting event in the United States, 1875.

http://espn.go.com/horse/TripleCrown02/s/Kentuckytraditions.html

It is the jousting tournament held at Natural Chimneys in Mt. Solon, Va. This event is held every year in August. I think they are up to 140 years now.
http://www.nationaljousting.com/fame.htm

There seems to be quite a few that are laying claim to this one:

Over 130 years later, the "Run for the Roses" at Churchill Downs is the oldest continually held sporting event in the United States.

Take, for example, the Kentucky Derby , the oldest continually held sporting event in the United States.

https://en.wikipedia.org/wiki/Aristides_(horse)

http://www.boston.com/travel/articles/2006/08/09/sporting_impressive_history/

On the third Saturday in August every year, a jousting tournament is held at Natural Chimneys. This is the oldest continually held sporting event in the United States.

https://en.wikipedia.org/wiki/Mount_Solon,_Virginia

Though it does look like the first post is the most accurate.

The first America's Cup was held at the Isle of Wight, England in 1851, not in the USA. It isn't always held in the USA.

https://en.wikipedia.org/wiki/America%27s_cup