One interesting puzzle being pursued by scientists is the question of whether life is more-or-less inevitable given the right circumstances, or whether it is a fluke.
The answer impacts, for example, our educated guesses as to how probable life may be on other planets -- if life is inevitable, or common, or easy, then all we have to do is find evidence of enough planets and we can think it likely life exists elsewhere in the universe. If life is unlikely, then we are less confident and must rely more heavily on the mathematics of large numbers.
If life is inevitable, then one would think it would have arisen on Earth more than once; several times, really. It is clear that life is relentless once established -- it reaches into every nook and cranny of the world, no matter how improbable. But the evidence seems to favor the idea that all the life we know of on Earth is genetically related, and therefor of a single origin -- of a single instance of the kick-starting of life on Earth, from which we all descend.
Casual, hobbyist sorts of observations can help us think of this problem. For example, why does everything have five fingers and five toes? (First, why five in particular? It's a strange number; we are bilaterally symmetical creatures, and five doesn't bilateral. I like to joke that God's intelligent design is improbable on this basis: Five fingers is excessive, even cartoon creatures manage to get by just fine with only four fingers; three arms and three hands would have been much more useful...)
But my point is that it's not just us, but every land animal has five digits. Only octupii and starfish have limbs of a different order. This suggests a single, or at least limited number, of life originations.
Scientists are following up on this by taking more pains to check the genetics of the odder sorts of creatures closely. (See "Are There Aliens Among Us?" in Scientific American, Dec. 2007) One notion is that life may have arisen several or even many times, but some life forms died out, and others were pushed aside by the current dominant form. To check this, scientists are looking into the remotest and most hostile areas of the planet--seafloor volcano vents, subAntarctic lakes--seeking genetically distinct creatures, on the speculation that if prior forms of the arts of living survived, they would likely do so in the remoter Icelands and Tierra del Fuegos and Pyrannees of life's world.