I think what does it for me most is human consciousness. Some people call it the spirit. George Lucas called it "The Force" ;-).
Whatever you call it, it seems to transcend the basic reality of the physical world. Some people have already claimed to have done so. Science has yet to explain it, much less duplicate it, but that's not to say they won't. The way I see it, science is nothing more than a belief system, which requires its own leaps of faith and its own denominations which adhere to their doctrines just as tightly and fervently in the face of contradicting information as a religious zealot, to the point that it can take generations for new beliefs to take-hold, only to be changed again by future generations. One era's scientific fact is a future era's apology to textbook and encyclopedia writers.
Atheists balk at this concept usually, the idea of science as a belief system because of the scientific method. Yet so much of science operates on theory and principle that it ceases to be concrete and deluding yourself that it is, isn't much worse than the creationist who insists the world was made in 6 days because a couple of ancient books say-so.
I think the important thing to remember is that science and religion attempt to explain two very different things and don't necessarily need to be at odds with each other. On the one hand, science makes an attempt to explain how things work. Religion, on the other hand, makes an attempt to explain the "Big Why": why are we here and for what purpose?.
Some people of science have little use for the notion of why and for what purpose and choose to discard the notions entirely. Since it cannot be explained by science it must not exist.
Some people of religion have little use for the notion of how things work and similarily discard the notion entirely. Since it cannot be divined from the texts of yore, it must be the work of God with which man would be wise not to tinker.
I find either view a little limiting.