Several days of nationwide rioting in Greece has shut down most flights into and out of the country. If you have plans to travel to Greece, contact your airline to find out what changes will be made to your itinerary.
The U.S. Embassy in Athens has also issued a travel alert for all Americans, urging them to "avoid the areas of demonstrations, and to exercise caution if within the vicinity of any demonstration or large crowd." Citizens should also "stay current with media coverage of local events and be aware of their surroundings at all times." Further, it seems that most internal services within Greece—hospitals, post offices, and so forth—have been shut down.
There's no telling how long the situation in Greece will persist. If anything, the rapid and severe escalation of rioting (triggered by the shooting of a 15-year-old boy by police) suggests things will get worse before they get better. If you plan on traveling to Greece even within the next few weeks (around Christmas, for example), contact your travel providers and your credit card company if you booked with a credit card. And as the embassy suggests, pay close attention to the news.