If you've watched any of the popular science programmes on the Higgs boson you've almost certainly got the wrong idea about it. In particular, the title to your question suggests you've heard the description "God particle" once too often since the Higgs isn't the root of all elementary particles.
Physicists believe that particles acquire mass through a process called electroweak symmetry breaking. I'm not sure that this has been proven, but the theory fits observations so well that everybody believes it. Anyhow, the Higgs mechanism is one of many mechanisms by which the symmetry breaking could occur. Actually it's the simplest and most elegant mechanism, and all the other suggestions have various problems associated with them, so most people's money is on the Higgs, especially now there's a hint of it at the LHC.
But there are various other possible mechanisms including a composite Higgs theory known as the little Higgs, and it's possible that experiment could prove the little Higgs theory to be correct. Alternatively another symmetry breaking mechanism like Technicolor, that doesn't have a Higgs boson at all, could turn out to be correct.
So while it currently seems most likely that the simple Higgs boson model is correct, the Higgs might not be a fundamental particle or might not exist at all. At the end of the day electroweak symmetry gets broken and particles acquire masses, so all the alternatives to the Higgs have to do basically the same thing. Failing to find a simple Higgs boson wouldn't be the end of Physics.