What situations have resulted in expansion of presidential powers?
Presidential powers in the United States have expanded dramatically since the framing of the Constitution. Congress was originally intended to be significantly more powerful than the President, but gradually the Executive Branch has assumed greater powers.
Andrew Jackson was a pivotal figure due to his use of his popularity and prestige to amass personal power, in particular by his use of patronage or the "spoils" system in which he used his power to make appointments to reward supporters rather than choosing people based on qualifications. He also made unprecedented use of the veto system. One important situation was the nullification of a federal tariff law by South Carolina where Jackson used presidential powers to assert federal power and prevent nullification.
Abraham Lincoln used presidential powers during the Civil War to suspend habeas corpus and expand the army. He justified this expansion of presidential powers by the emergency of the Civil War.
Theodore Roosevelt expanded the use of executive orders in response to both issues of foreign policy and in response to widespread corruption and "robber baron" style businesses that were harming citizens through price collusion, monopolies, selling harmful products, etc.
Woodrow Wilson expanded presidential powers in response to World War I, seeking greater power in response to the need for the US to have a larger role in international affairs.
Franklin Roosevelt also expanded presidential powers in response to two emergencies, the Great Depression and World War II.
Basically, presidential powers have expanded during times of crisis. This has been seen most clearly in times of war, but it was also seen in the Great Depression.
During times of crisis, people seem to want strong leadership. They look to the president as the one identifiable leader who can get them out of trouble. They tend to feel that it is okay to give him more powers than usual so that he can get them out of the crisis.
The two biggest crises since the Civil War both involved Franklin D. Roosevelt and saw him expand presidential power. These were the Great Depression and WWII. In both cases, the size of the US government expanded greatly and with it the power of the president as the leader of that government.