Political drafts are used to encourage or compel a certian person to enter a political race, by demonstrating a significant groundswell of support for the candidate. A write-in campaign may also be considered a draft campaign.
America has seen many draft movements in its history. Maybe the most notable draft campaign was that of President Dwight D. Eisenhower. Draft Eisenhower movements sprung up in both parties in 1948 and again during 1951. Eisenhower did his best to ignore them.
In late December, then President Harry S. Truman wrote to ask General Eisenhower, "I wish you would let me know what you intend to do," and General Eisenhower replied, "I do not feel that I have any duty to seek a political nomination." Not too long after, General Eisenhower reconciled his commitment not to seek a political office by taking the position that he would be personally compelled to respond if called to a higher duty.
Henry Cabot Lodge forced the issue by entering Eisenhower in the New Hampshire Republican primary without Eisenhower's authorization ... General Eisenhower won all the Republican delegates and soundly defeated Senator Taft (who had campaigned intensively in the state) by a vote of 50% to 38%.
After the primary win, Eisenhower told a reporter, "Any American who would have that many other Americans pay him that compliment would be proud or he would not be an American." Convinced of being called to a higher duty, he announced his candidacy the next day.
Most recently, the candidacy of General Wesley Clark, came from result of a draft. Clark, who recently retired from the military and took a job as a CNN military analyst, had no intention of running until multiple "Draft Clark" sites came up on the web urging Clark to run. Over about a two month period the draft became a nationwide effort due to TV coverage and the use of the internet. In September 2002, Clark said he would make up his mind on whether to accept the draft or not in the near future. Not too long after that statement, Clark announced his candidacy in his hometown of Little Rock, Arkansas, citing that he was pulled in by the people to run for the presidency.
Mentionable is the current draft campaigns of Al Gore and Hillary Clinton. While both Gore and Clinton have said repeatedly they would not seek the nomination, neither has disclaimed interest in the idea of a draft.