What kind of precedent would it set if Greece's debts were forgiven? Would there be any willing future creditors should another (very likely) financial crisis arise?
Globally? None. This has happened before (even in similarly developed countries - see Argentina) and will happen again.
For Europe? It's now clear that countries in the euro zone can default. A few years ago this was associated with the risk that private lenders will turn away from other Southern European (Portugal, Italy, Spain) countries, in turn raising their interest rates and thereby also pushing them into bankruptcy. Now that most debt of Greece is owned by either the ECB, EFSF or the IMF and the bond markets seemed to be back to business as usual this isn't a huge risk anymore.
Long term it might mean that lenders will do some due diligence even for countries of the euro zone (then again, many of them got to sell the Greek bonds at full value to the ECB, so who knows...)
Edit: As you wrote "forgiven" - debt is usually not forgiven but renegotiated once the indebted country stops (or threatens to stop) servicing said debt in the hope that an agreement can be found which is better then a unilateral default.
Also, the debt run up by a US-supported Greek dictator is “odious debt”, and not owed by the population. (http://www.euronews.com/2015/04/17/chomsky-says-us-is-world-...)
Please notice that loans come with an interest rate, which varies accordingly to the supposed risk they present. That means that any creditor lends money explicitly accepting the potential risk of not being repaid, compensated by compound interest.
There are many precedents. In fact most countries did failed their debt at some point, the real matter here is politics: the Greek case has been managed in the most insane way, and the Troika simply want to put the fault on someone else. However Tsipras and al weren't governing back when Greece was (against all odds and reasons) accepted in the Eurozone; they weren't when the Troika decided to bail out the French and German banks instead of refinancing the Greek economy; so they're actually quite entitled to their refusal of bearing others' misdeeds.
Debt are forgiven all the time. In fact IMF and co should do more forgiving because they loaned at unfare rates to countries in Africa that had 0 financial expertise or were ruled by bloody dictators. Why should the people pay for that? they shouldn't. Themselves have been scammed and the money is stashed in Swiss accounts while the common people saw none of it.
The situation of Greece is off course different except that it's really a moment where we will see whether EU is the real thing or it's just every country for itself. If the latter then it's not going to work much longer. It will be the end of the EU.
If any country can default their debt without consequences I leave it to you to imagine the new crazy interest that a EU country will have to pay given the "risk" of a default. That's pretty bad for the three country mentioned above.