What rights do you have?

The issues of treatment of terror suspects and illegal immigration have got me wondering what rights people have. I'm not talking about U.S. citizens on U.S. soil - the Founding Fathers made that pretty clear. I'm also not looking for a discussion on what rights should one have; there are plenty of places to do that already.

For instance, does the Fourth Amendment apply when an American soldier is searching a home in Baghdad? (Again, forget whether it should - I'm sure everyone has an opinion on that - I certainly do.) Does the analysis change if it's an MP searching a soldier's trunk for contraband at a base in Afghanistan?

Let's bring this a little bit closer to home. Let's say a sheriff's deputy in Arizona watches a car with Mexican plates sneak across the border. He suspects drug smugglers and stops the car. What does he need in order to search the vehicle? How about an F.B.I. investigation into a suspected terror cell: the Bureau wants to tap the phone of an Iranian student who overstayed his visa. What do they need in order to accomplish that?

Do the protections guaranteed by our Constitution extend outside the borders of the U.S.? Within our borders, do they extend to people who are not legally here?