...It's easy to confuse these things, of course, because Bitcoin is the name for both the software system and the currency used in that software system. The two should be understood separately, and the latter derives its original value from the former, and it's long-term value from the supply and demand of that original value...
Bitcoins also have some physical unique properties. It "backs" itself, as its price its showing.
I propose backing BitCoins with their own awesomeness.
Bitcoin as a concept/software brings value to people, and a lot of this value is currently reflected in the market price of bitcoins because there are currently no other Bitcoin-like currencies. In other words, there is a demand for the valuable Bitcoin concept/software in a currency and bitcoins are currently the only supply. However, many other Bitcoin-like currencies will come along and effectively increase the supply of currencies that can deliver the value of the Bitcoin concept/software. I believe the growth in supply of currencies offering Bitcoin-like properties will be able to greatly out pace the growth in demand for currencies offering Bitcoin-like properties. This is why I proposed this backing solution because I believe it is desirable to back the actual bitcoins with something of long term value rather than depend on the Bitcoin concept/software as the only foundation for the value of bitcoins.