Non-carbon based life forms?

It's theoretically possible. But carbon has such incredible chemical properties that it's by far the best choice. Fiction, of course, has no such restriction. Why not just hypothesize a way to alter silicon to confer to it similar properties? Perhaps silicon-based fungus or mold starts showing up in places with very strong magnetic fields or at very high temperatures or in the presence of fluorine.

This is a very interesting question, but I don't think that science has the tools to answer it... yet. The difficulty is that we still don't have a definite description of how carbon based life developed from non-living materials on this planet. It turns out that this is a very tricky puzzle to solve for forms of life that we KNOW about and that we can study in a lab. We need more time and more research (funding?). To me, it seems like it would be much trickier to figure out a mechanism that would allow a carbon-based species to change in a stepwise way to a non-carbon-based species. Especially, when you consider the fact that the speciation we see on earth occurs through genetic changes, NOT through changing the molecules (and atoms!) that make up the DNA itself.

personally, i think organisms on the earth are water based (going on a mass basis).

but to address your question, carbon has unique properties (like the ability to assemble into large, stable polymers) that other elements lack. silicon has some properties similar to carbon but it is too different to substitute for carbon in the way we understand the contribution of carbon chemistry to metabolism.

one example - carbon dioxide is generated from the oxidation of fuels and exhaled as a gas. silicon oxidized in such a way would produce silicon dioxide (hard to exhale) http://en.wikipedia.org/wiki/Silicon_dioxide

Yes it is possable to have life forms out of silicon as silicon as similar properties as carbon although silicon based lifeforms would be tough as old boots

To say no would be as daft as to say there was a God or indeed, there is no God.

In a Universe as vast as it is, we are but a spec of time so insignificant that surely the theory: "Given infinite time, infinite possibilities are possible" must surely be true ?

Edit: Thank-you Frank ... Learn something every day, even if I would pick up on "in a way we understand" as usable in a Science Fiction manner.

No. Every organic thing that has ever existed is carbon-based. On other planets however- that's a good question.