What percentage of the hydrogen today has never been in a star It stands to reason that some of the hydrogen and helium that formed directly as a product of the big bang might never have fallen into a star to re-ejected when that star explodes.  My question is, given the best theory, what percentage of that matter has managed to drift without being sucked into a star.  Do we have any idea?
About 70% of the baryonic matter in the universe is hydrogen, with a mean density of about $4\times 10^{-29}$ kg/m$^3$.

Most of the stars that have ever been born are still alive, since an average star is only about $0.25 M_{\odot}$ and has a lifetime much longer than the age of the universe (so very little material has actually been recycled). 

If we assume there are $10^{22}$ stars of $0.25 M_{\odot}$ in an observable universe of radius 47 billion light years, that are 70% H by mass, the "stellar" hydrogen is only one part in 73.

So, there is only one hydrogen nucleus (a proton) in a star for every 73 in the universe. This ratio would have been smaller in the past (E.g. when theSun was born). But as I mentioned, most of this hydrogen (about 90%) is in stars that are longer lived than the universe. Therefore my very rough estimate is that around 1 hydrogen atom in every 1000 on Earth has been inside a star. This contrasts markedly with say that 100% of carbon and oxygen atoms have been inside a star.

EDIT: To be fair, this calculation hinges a lot on how many stars there are in the observable universe. This number is very uncertain and could be higher - perhaps $10^{23}$ (see here), in which case my numbers are somewhat pessimistic and it might be more like 1 H atom in 7 is inside a star and 1 H atom in about 100 on Earth were inside a star. However, I don't think there is any argument that the majority of hydrogen in the universe is not, and has never been, in a star, but whether that is 90% or 99% is still moot.