I'm no expert, but I had similar questions as you and so far I see no reasonable responses really explaining the issue clearly So I will try my best with my limited understanding, without any politicized agenda. (I'm not an economist, as you may tell from the language and way I explained things, but I read a lot and this is the understanding I've come to, and hopefully it helps your grasp on the situation. I hope real economists can reply and correct any inaccuracies or outright falsehoods here. I also request that any biased posters who have agendas to stay out)

The Federal Reserve issues bonds in order to raise money. Investors or savers, such as China, US taxpayers, or foreign investors, buy those bonds, effectively lending money to the US Gov't.

Where did that money come from? The US Central Bank (The Federal Reserve) has the power to expand and contract the Dollar Supply. They do this through fractional reserve banking. Yes, you're right, when there is more debt than money to pay it, people default on their loans, and that is what we call a contraction. The bank must write off that loan, essentially removing the money from the balance sheet. It's a tough time for the economy as there is less money flowing around, but its also inevitable under our current system. Loose money, tight money - these are the business cycles we must live and work with.

As for the world economy, we truly live in a global age: banks in China, Europe, the US, the Middle East, lend and borrow from each other daily. Why would a country borrow to such an extent that it seems as if they can never pay it back, like the US $15 trillion deficit, for example?

Pretend you're a student going to college. You borrow $200,000 in student loans (perhaps an unwise choice, but follow along), with the implicit expectation that you will pay it back with your future earnings. That, essentially, is what debt -and even money- represent. Money is a claim on resources. Debt is a future claim on resources.

So if foreign investors hold US debt, then they hold a future claim on the productivity of the US workforce. This is resolved when the US pays off its debts, based on tax income it receives in the future, not much unlike a student borrows money for college, then pays it off in the future.

How is it possible that EVERYONE owes so much money? Whose money is it?

This is a complicated question to which I initially wrote a reply but removed it as it was inadequate. I hope someone knowledgeable can illustrate this concept for us.

Now lets examine your observation that every country on the news is in some form of 'crisis'. We must consider that only countries in crisis would appear on the news, omitting the stable countries. If a country borrows money, you can be sure someone, somewhere, is lending or providing it. Therefore there must be lending countries or people. If a country cannot pay off its debts, the lenders lose that money, which is why you may have heard of the hubbub about China's desire to sell off their trillions of $ in US bonds: they are worried about the stability of the dollar.

Now lets talk about the stability of our currency, a subject that is never explained much in school (at least to me) - perhaps because this generation in the US is in a unique position to have never experienced such a phenomenon.

Currencies, from our vantage point, seem stable. Sure there is inflation - the steady, slow rise in prices from year to year - but there are no wild, drastic changes to the US dollar. At least there haven't been. We may not realize how lucky we are. In Argentina, their currency used to be so unstable that some grocery stores stopped printing prices on their food because from the time someone picked up some bread and brought it to the checkout line, the price had already jumped significantly. So why do currencies remain stable, while some fluctuate wildly?

Because the US economy is highly prominent and respected, and the US $ is backed by the US government, and based on the productivity of the US workforce. Because a currency is only as good as the government and working citizens that back it, countries simply do not expect the US to default on its debt. They have confidence in our system and our promises, so they expect to get their money back (with interest). I can't emphasize this point enough, because while simple, it truly is profound in its significance and so I will repeat it: the currency is only as good as the system and people that back it. If one day God forbid, the US system should become untrustworthy - either the government officials in charge act irresponsibly (borrow excessively, inflate excessively, etc.), or the citizens stop producing - then the faith and trust in our way of life, our system, and our future, will all be placed in jeopardy. Which means the dollar is in jeopardy, because the trust has been damaged. Money is inherently worthless: it functions only if people have faith in the institutions backing it.

How is this ever resolved? You may want to look at examples of currencies in history and how they fared. No one can predict the future, of course, but if you study other currencies' histories you can foresee most of the possible ways this can unfold.

One option available to the US government (or rather, the Central Bank), is the ability to inflate and contract the money supply at will. They were given this power in 1917 after several "shocks" during the late 19th century. With this power they thought they could fiddle with the money supply in order to prevent severe economic downturns. This 'central bank fiddling' is called Quantitative easing, and its a kind of 'monetary policy'.

(There are two ways the powers that be have to fiddle with the economy: monetary policy and fiscal policy. Monetary policy refers to actions taken by the central bank. Fiscal policy refers to actions taken by Congress, such as setting the tax rate, etc.)

Now on to the possible directions, and this is delving into the murky realm of speculation (and based again on my non-expert opinion).

1. Lets first assume that the US doesn't default on its debt. Therefore the debt must then be repaid. So using the tools we have, the Central Bank could A) inflate the money supply. or the US Government could B) set higher taxes and/or reduce expenditures.

Lets look at option A. The Central Bank, as I explained, was given the power to combat severe economic downturns such as the one the US economy is currently in. The Fed is currently using quantitative easing to expand the money supply (which can lead to inflation. whether it always does, I'm unsure - perhaps an economist can explain). You should read the wikipedia page for QE, but basically the Fed sells bonds (they loan money) to give banks more reserves, which the banks are supposed to pump into the economy. This is supposed to lead the economy out of its downturn, which will put the US in a much better financial situation. Economic growth = greater productivity (theoretically at least) and thus greater ability to pay off debt.

So who pays for the debt? If the money supply inflates, lenders/savers end up paying for the debt through the decreased value of their loans/savings over time.

Option B is for the US gov't to take fiscal measures: increased taxes, reduced spending. In fact the gov't could pay the debt quite quickly if everyone contributed to the deficit. But as life goes, coordinating millions of actions is difficult, especially with such a divided citizenry as we have now. As you know, Congress is currently debating whether, and how, to increase the tax rate or reduce spending. And sometimes it may seem as if there is no progress being made at all, our political opinions are so divided. But if we assume the debt must be repaid, then it has to be repaid somehow, and if the US citizenry doesn't pay for it now either through increased taxes or reduced spending, then we must pay it in the future, meaning our children and possibly their children must pay for it.

2) The US defaults on its debt. I'll leave this to others to fill in. Lets just say that the only thing keeping us from devolving into anarchy is the combined trust and willingness to participate in the system we have. So what happens if the system collapses? If the dollar no longer is accepted? Examine the possibilities and that will be your answer.