Pretty sure C-130 does, and probably will, hold that record.
EDIT*
"The C-130 family has the longest continuous production run of any military aircraft in history. In 2007, the C-130 became the fifth aircraft—after the English Electric Canberra, B-52 Stratofortress, Tupolev Tu-95, and KC-135 Stratotanker—to mark 50 years of continuous use with its original primary customer."
B-52 holds it apparently, and the Air Force is planning on keeping them until 2040 too.