Travel Warnings are issued to describe long-term, protracted conditions that make a country dangerous or unstable. A Travel Warning is also issued when the U.S. Government's ability to assist American citizens is constrained due to the closure of an embassy or consulate or because of a drawdown of its staff. The countries listed below meet those criteria.
Somalia 10/24/2008
Sudan 10/02/2008
Pakistan 10/01/2008
Israel, the West Bank and Gaza 09/26/2008
Yemen 09/17/2008
Iran 09/15/2008
Georgia 09/10/2008
Lebanon 09/10/2008
Afghanistan 09/10/2008
Algeria 08/22/2008
Kenya 08/22/2008
Colombia 08/07/2008
Congo, Democratic Republic of the 07/23/2008
Saudi Arabia 07/09/2008
Uzbekistan 07/03/2008
Chad 06/23/2008
Sri Lanka 06/13/2008
Iraq 06/13/2008
Eritrea 06/11/2008
Cote d'Ivoire 06/09/2008
Nepal 05/07/2008
Haiti 04/30/2008
Burundi 04/22/2008
Syria 04/15/2008
Central African Republic 03/25/2008
Philippines 02/13/2008
Nigeria 10/30/2007
Links are orphaned, source Here
As far as I know, the only place that the State Department forbids travel to is Cuba.