Trump has never served in the military. Selective Service records obtained from the National Archives by The Smoking Gun in 2011 reveal the following history of his draft eligibility:

Donald Trump became eligible for the draft on his 18th birthday (14 June 1964) and registered with the Selective Service System 10 days later. He received the first of four 2-S (college) deferments on 28 July 1964.
Trump received his second college deferment on 14 December 1965.
Trump’s previous deferment expired and he was reclassified 1-A (available for military service) on 22 November 1966. His 2-S deferment was renewed on 13 December.
1967:  No record.
1968: Trump received his fourth and final college deferment on 16 January 1968. After graduating from Wharton, he was reclassified 1-A on 9 July 1968. Trump underwent an Armed Forces physical examination (with a result listed only as “DISQ”) on 19 September 1968 and was reclassified 1-Y (qualified for service only in time of war or national emergency) on 15 October 1968.
According to a statement from the Trump campaign, the 1-Y classification stemmed from Trump’s having bone spurs in both heels:  “While attending the University of Pennsylvania’s prestigious Wharton School of Finance, Mr. Trump received a minor medical deferment for bone spurs on both heels of his feet. The medical deferment was expected to be short-term and he was therefore entered in the military draft lottery, where he received an extremely high number, 356 out of 365.”

 

1972:
Despite the supposedly “short-term” nature of Trump’s disqualifying physical condition, on 17 February 1972 he was reclassified 4-F (not qualified for military service), presumably due to the abolishment of the 1-Y classification the previous year.