No one is above the law, not even the president

We are a nation of laws, or we are nothing
We are a nation bound to a Constitution that was ratified 217 years ago, which went to great pains to create checks and balances designed to differentiate this new nation from the monarchies of Europe. That Constitution was first amended with the Bill of Rights in 1791 and only amended 17 times since.
In other words, it has stood the test of time. Judges and scholars, legislators and citizens can argue over whether the Constitution should be interpreted strictly or liberally, but no one can argue that it was designed to give a president the powers of a king. Indeed, many of the amendments in the Bill of Rights were inspired by excesses by agents of the crown of England that were well known to the framers of the Constitution.
In the case of the Fourth Amendment, two of those cases involved the warrantless seizure of papers from pamphleteers who were openly critical of the government -- and the papers of friends of those pamphleteers.
The answer
The Fourth Amendment declares that the "right of the people to be secure in their persons, houses, papers and effects against unreasonable searches and seizures shall not be violated and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
Gerard V. Bradley writes in "The Heritage Guide to the Constitution" that "by requiring probable cause and a particular description of the place to be searched and the things to be seized, the Framers prohibited rambling intrusions and rummages into people's belongings." He describes the Fourth Amendment as "the constitutional sentry whenever someone's privacy is diminished by a governmental search or seizure."
President Bush is ordering the sentry to stand down. Citing his power as a wartime president and his responsibility to protect Americans, the president is claiming authority to conduct electronic surveillance against a citizen of the United States without a warrant or any kind. Arguably, if he can tap a phone without a warrant or read computer messages, he can climb through a window and rifle a desk, with impunity.
Of course, while the general locution is that the president authorized eavesdropping without a warrant, in practical fact, George W. Bush won't be deciding whether or not to tap your phone. That decision can be made by any number of people, down to a shift supervisor at the National Security Agency. It may well be a prudent decision, based on solid probable cause, or it could be a fishing expedition based on the flimsiest thread between your phone and that of a presumed terrorist. Regardless, it would never be subject to the checks and balances that the Founders were careful to put into the Constitution.
A check on power
The government has enormous power over us. The power to peak and probe. The power to tax and take property. The power to imprison us, or even to take our lives. But the Constitution requires the government to follow due process before it imposes itself on us.
The White House already had a compliant secret court that historically provided warrants in the interest of national security. The 1978 Foreign Intelligence Surveillance Act even gave the government the ability to wiretap now and ask permission up to three days later.
But the White House found even this to be too restrictive, or simply inconvenient. So it decided to make up its own rules.
There are those who are untroubled by these developments. They do not believe they could ever be subject to a warrantless tap. Perhaps that's true of someone who lives without talking or corresponding with a friend, relative or business associate from outside the United States. Assuming, of course, that this administration or any that follows does not decide that national security demands it begin spying on anyone who talked to anyone who talked to anyone who might have terrorist ties.
Constitutional checks are designed to keep that from happening. When a president is allowed to say he is the sole arbiter of what must be done to protect the nation and its people, we've started down a dangerous path. If we don't honor the rule of law, we not only forfeit our rights as citizens, we forfeit the right to hold the United States out to the rest of the world as a beacon of democratic governance. We forfeit the Founders' dreams of creating a nation that was different from any they knew.