One thing I've seen a reference to from time to time is a supposed refutation of evolution on the grounds of (im)probability. The argument goes that organic molecules being assembled into complex and reproducing forms is so improbable that the universe, let alone the earth, is simply not old enough for it to have happened.
One could counter this argument a few ways. The age of the universe might not be what we think it is. We don't know, for sure, what the actual improbability is. Heck, we're still working out how living systems, things we have working examples of, actually work. There are likely a whole lot of "Duh! It makes sense now! How'd we miss that for so long?!" moments ahead in biology. But the thing that annoys me is that the argument requires a fundamental misunderstanding of probability.
( About Probability )