I'm not sure any country today is experiencing total anarchy, because they probably wouldn't be countries. Some that are in extreme turmoil could be afghanistan, Libya, and the sudan.
The more modern usage is "Failed State", meaning that there is no functioning central government. This usually results in a state of anarchy being prevalent.
Somalia is a good example of a country currently in anarchy. Yemen and the Democratic Republic of Congo are pretty darned close.
KabobTown is an anarchy though