How on earth are bitcoins "created?" Obviously notes and coins are created by States and are backed by the State, silver and gold have both practical uses and value given by public demand.
Professor John Quiggin of the University of Queensland has noted that since Bitcoin by design has no intrinsic value, it is "perhaps the finest example of a pure bubble" currently known, from what I know I'd say that he is entirely right.
They are created by solving cryptographic problems, you crunch numbers until you find a coin by being the first to find the next number (coin) in an increasingly hard to calculate sequence. The coin you find (you can install the software to find coins on your pc) then becomes a permanent part of the market. As more are found, the work required to solve for the next coin increases, so that no matter how fast computers get, new coins are created slowly.
In that sense they are backed by the cost of the electricity required to find the next coin. With very efficient computers, it currently costs hundreds of dollars in electricity to find the next coin. Thus at some level, bitcoins cost energy to produce, via computers. This makes them rare.
The cleverness of the system is that this number crunching to earn the next coin also inherently checks all the posted transactions to prove that they are legitimate, meaning that the "miners" who are trying to find the next coin are also providing a service to everyone else that makes the bitcoin trading markets reliable.
No currency has intrinsic value now that we have abandoned the gold standard. They are backed up by your trust in a system. In the case of bitcoin, that system is believed provably secure using contemporary mathematics.