The Fifth Amendment to the Constitution of the United States outlines a citizen's protection against self-incrimination: "nor shall be compelled in any criminal case to be a witness against himself..."
Your statements may be used against you
Once you have been placed under arrest, if you are to be questioned further, you have to receive from the law enforcement officers a notification of this right. Not only should you be notified of this right, but if you say something self-incriminating before you receive this warning, these statements may not be used against you.
Spontaneous utterances can be ruled as unprotected by the 5th Amendment
However, spontaneous utterances to police (especially those statements captured on videotape) can be devastating to the case against you if they are ruled to be unprotected by the Fifth Amendment.