We learned it back in ninth grade Civics class. Our political system is based on checks and balances. Neither house of Congress can pass a law without the agreement of the other house. Laws passed by both houses of Congress are subject to presidential veto. A presidential veto is subject to a congressional override. A law that makes its way through that process is subject to judicial review, and may be found unconstitutional by the courts. The politicians can amend the Constitution to reverse the effect of a court decision. And so on, and so on.
But a president or governor can make some decisions totally on their own, in relation to which the political process has no formal check. Here are links to two current media reports regarding such powers, the president's pardon power, and a governor's ability to make an interim appointment to a vacant U.S. Senate seat.
However, as the old saying goes, actions have consequences. The voters can pass judgment on such decisions at the next election. For example, Gerald Ford was denied a full term as president in 1976, in part because he had pardoned Richard Nixon in 1974. And after a popular governor of Minnesota, Wendell Anderson, in effect appointed himself to a U.S. Senate vacancy in 1976, the voters gave his opponent, Rudy Boschwitz, a landslide victory over Anderson in the 1978 general election. As I found out to my chagrin when I worked on that campaign as an Anderson volunteer, many voters deemed that "self-appointment" to be a sign of arrogance.
But, if an executive is about to leave office under term limits, as is the case with both President Bush and Delaware Governor Minner, even that sort of check is inapplicable. The main remaining consequence is the verdict of history.
As you can see in the Times piece to which I linked above, Bill Clinton is still dogged by criticism of pardons that he granted as his presidency was ending in 2001.
On the other hand, the verdict of history has acquitted Ford. By the time of his death in 2006, there was widespread acknowledgment that his pardon of Nixon was a statesmanlike act.
Here is a link to the constitutional provision allowing presidents to grant pardons (see Article 2, Section 2, clause 1).