"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, …."
You might think that means the government can't clandestinely search your e-mail, but it doesn't.
Suppose you use Gmail or Yahoo! mail. If the government wants to see your e-mail, it can have the warrant served on that company. Of course, the service provider has to respond to the warrant, just as you would if the feds came to your house. The difference is that the company decides whether to resist the court order, not you. You are supposed to be informed within 90 days, but in practice you may never know. E-mail stored elsewhere really isn't yours.
In 2005, The New York Times exposed a program of "warrantless wiretapping" of communications, including e-mail between individuals in the US and foreign countries. Congress codified the legality of some such searches in 2007 and again this summer. In a word, the rules change when "terrorism" is invoked as a justification. If the government demands your e-mail using a National Security Letter, your service provider is prohibited from telling you.
Searching e-mail as it crosses the US border is perhaps analogous to inspecting a laptop carried into the US Customs officials can inspect (and confiscate) your possessions; arguably they should also be able to search your e-mail – though under antiterrorism legislation, the eavesdropping can happen without your knowledge.
What about purely domestic e-mail surveillance without a warrant? The Terrorist Surveillance Program processes domestic e-mail in cooperation with Internet service providers; the Electronic Frontier Foundation has taken the government to court. But eavesdropping occurs even for nonterror-related crimes.