Over the years there were quite few individuals who were rumoured or believed to actually govern without being President. "Shadow President", "Real President" etc.
Some notable instances:
1. First Lady Edith Wilson, after President Woodrow Wilson suffered a debilitating stroke in late 1919.
2. Sherman Adam, who was the Chief of Staff to President Eisenhower (who liked to delegate powers to his aides) and, arguably, the most powerful one. There was a popular joke back in 1950s:
3. About Ike again: some argued that he essentially abdicated foreign policy to his Secretary of State (Dulles) and domestic affairs to the Senate Majority Leader (LBJ).
4. It's widely believed (and well documented) that during last months of Nixon's Presidency it was Alexander Haig who ran the government, with President being preoccupied with the Watergate scandal.
5. Donald Regan was another example of powerful Chief of Staff (1985-1987) and his position was frequently compared to one enjoyed by Prime Minister in other political systems. When President Reagan (another one who liked to delegate) was briefly out of power during surgery, Vice President Bush was formally the Acting President, but media considered that Regan ran the show.
6. Ah yes, Dick Cheney. To some critics, he was President in all but name.
Any other historical examples? Discuss