According to Official Guinness Records,
The longest running horticultural show is The Philadelphia Flower Show, which has been hosted annually by the Pennsylvania Horticultural Society since 6 June 1829 in Philadelphia, Pennsylvania, USA, with the exception of 1918, and 1943-46, due to the US involvement in World War I and II. The exhibitions have been held in in various indoor venues in Philadelphia. The next show in 2006 will be its its 172nd (taking into account the war years), but celebrating its 177th anniversary. The first show, held in 1829, was called: The Exhibition of Fruits, Flowers and plants.
For a complete list of 1829 records, please visit 1829 Guinness Records in United States.