You don't want to ask the question because it feels selfish when a whole country's economy is half-past the brink of collapse. But you're asking it anyway, probably with good reason. Maybe you already have a ticket, or your sister's been pestering you to go with her. Honestly however, the situation is Greece is tenuous, but it should still be safe for a traveler provided you take the proper precautions.
Bad News
Right now the economy is extremely tenuous. Trust in banks is at an all-time low. In some places, ATMs work fine. In others, they're running dry. With the banks in peril, there is a very real possibility that credit cards will no longer work, or if they do work, business may refuse to accept them. Many travelers are only carrying cash, but that, of course, leaves you vulnerable to mugging.
Good News
The upside for Americans visiting Greece is that the euro has tumbled in the wake of the crisis, and the buying power of the dollar is extremely high. Traveling to Europe hasn't been this affordable in a long time. Provided you're willing to rely on cash and live with some uncertainty, you're getting a great deal.
Bad News
There are protests pretty much daily.
Good News
Daily protests are just sort of a thing that happens in Greece, anyway. Amidst some tongue-in-cheek remarks, Dmitri Nikolaou told Cracked in 2014 that his mother has grown so accustomed to riots in the streets that she doesn't even flinch anymore when a police officer shoves her on her walk home. There are even websites to help you navigate riot-ridden parts of town.
Bad News
Since the "tourist-centric" areas of Greece include the islands off its main coast, if things do completely collapse while you are there, you might be a little bit stranded in the Mediterranean. While tourism companies and local hotels are painting a rosy picture, some visitors are telling stories about having to trade their iPads to cab drivers for rides to the airport in order to leave.
Good News
Your tourist dollars can actually help the situation. Outside money can only help to strengthen the Greek economy right now, and the hospitality industry is still going strong in the country. They know that they're currently Greece's best hope. The culture of hospitality goes back a long way, and you'll find that on the islands and in other tourist-centric parts of the country, daily life is almost untouched by the economic turmoil. Even if the worst does happen and Greece leaves the EU to return to the drachma, your dollars and euros should still be accepted.
The Upshot
Greece still has a lot to offer visitors, and people in the tourist industry are still waiting to welcome travelers to the country with open arms. That said, there is a level of instability and unrest that is undeniable. If you're looking to visit the country this year, be aware of what you're getting into by taking precautions and doing some homework.