According to Official Guinness Records,
The most concerts performed by a symphony orchestra is 14,000 by the New York Philharmonic (USA) over the last 162 years. The orchestra's archive has the first performance on 7 December 1842 and the 14,000 on 18 December 2004.
For a complete list of 2004 records, please visit 2004 Guinness Records in United States.