The US dollar is backed by the bullets and bombs of the US Military. Try to dump them and you'll get royally screwed. Just ask Qaddafi & Saddam.
Only correct answer so far.
You can make an argument that it's backed by confidence to repay debt and all that BS, but that confidence still boils stems from the US's military power. It's not that the world trusts the US to repay its debt, it's that the world knows the US doesn't have to repay its debts because: #1, if it goes down the drain the whole world goes with it, and #2, as long as the US has the biggest gun, the US will continue to make the rules.
This is why the US is so obsessed with "defense" (actually offense) spending and why we have a military budget that's more than the every other developed nation combined. It takes a lot of firepower to keep the rest of the planet under your thumb.