[El Gato]

From the state department's page on dual nationality.

U.S. law does not mention dual nationality or require a person to choose one citizenship or another.
...
However, dual nationals owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries. Either country has the right to enforce its laws, particularly if the person later travels there.Most U.S. citizens, including dual nationals, must use a U.S. passport to enter and leave the United States. Dual nationals may also be required by the foreign country to use its passport to enter and leave that country. Use of the foreign passport does not endanger U.S. citizenship.

[Alice in Wonderland]

As Ramli Hutabarat said, "It is about one's identity. One can have a 'split personality' because of dual citizenship."

[trumandogz]

while I own little allegiance to the country where I was born, I do hold a passport from that nation. I have only used it to travel to nations on business where either Americans are not welcome or where the US “recommends” its citizens not go.