Marbury v. Madison is important as it established judicial review. I've written about it a few times on here today, so will work in other answers. John Adams tried to game the process and nominated Marbury to a post in the final hours of Adams' administration. The hitch was that the Secretary of State had to deliver a commission to make it official. Thomas Jefferson's Secretary of State, James Madison (future President), refused to deliver the commission.
Marbury, who was denied the post, sued.
The outcome of the case is a little murky for casual readers. In essence, though, Marbury still got hosed. He was told that he should have received the commission and that Madison was wrong but that the actual act by which he was nominated wasn't properly constructed.
So, the Supreme Court won the day by reviewing the actions of the other branches and poor Marbury got nothing.
