Greece is a pretty small player in world politics, so ordinarily no one would care all that much about Greek economic woes. But fortunately for Greece - and unfortunately for the rest of the Eurozone - Greece is also a member of the Euro currency. If the Greek economy is allowed to continue imploding, it will sharply decrease the value and stability of the Euro, which will hurt the rest of the Eurozone economies - including such larger world players as France and Germany. It might also push over the edge some of the other wobbly members of the Eurozone like Portugal, Spain, and Ireland, and from there we'd see a giant domino effect. Bad mojo for everyone.
Also, if the Greek government defaults (i.e., declares bankruptcy), anyone who holds Greek debt stands to lose their money. Apparently a lot of Greek debt is held by French and German banks. It's conceivable that the banks would have to be bailed out by their respective governments in order to survive a Greek default, though no one really knows at this point. But in any case, a Greek default would suck for those banks, but would not (as I understand it) by itself necessarily have catastrophic effects for the rest of Europe. Except, of course, in conjunction with the the aforementioned collapse of the Euro.
So, pretty much everyone agrees that Greece should not be allowed to default. The problem is, all the potential ways to avert this disaster are very unpopular with pretty much everyone.