The Supreme Court this morning heard oral arguments in four same-sex marriage cases. It first heard 90 minutes of argument on the question "Does the Fourteenth Amendment require a state to license a marriage between two people of the same sex?" Here is the full transcript and the audio recording of arguments on that question. The Court then heard 60 minutes of arguments on the question "Does the Fourteenth Amendment require a state to recognize a marriage between two people of the same sex when their marriage was lawfully licensed and performed out-of-state?" Here is the full transcript and the audio recording of arguments on that question. A New York Times report on the oral arguments is titled "Gay Marriage Arguments Divide Supreme Court Justices."
UPDATE: Lyle Denniston at SCOTUSBlog has an excellent analysis of the oral argument.