Robin Hanson critiques the Doomsday Argument. This is an argument on the lifespan of the human species, which begins from the following principle: there is nothing special about present-day humans. "Therefore" we can consider the number of humans who have lived so far as a fraction of the number of humans who will ever live; the probability that this is between p and q is q-p. I put "therefore" in quotes because the implication is tempting, but one could equally well conclude that the amount of time there have been humans, as a fraction of the amount of time there will ever be humans, has this same distribution. (Indeed, I've heard both versions of the argument.) The first version of this argument says, for example, that the probability that there will be sixty billion more humans is at least one-half; the second says that the probability that we as a species will survive for another two hundred thousand years or so is at least one-half. (I'm assuming there have been sixty billion people who've ever lived and that our species is 200,000 years old.)
And indeed there are other classes of beings that you can use as the reference class here. Living things, for example. Or vertebrates, or living cells, or humans, or even such classes as "humans who haved lived after the year X", which get kind of ridiculous. That last one is particularly prone to abuse, as we can simultaneously say that humanity has a fifty percent chance of surviving past 2114 (if we take X = 1900) and past 3014 (if we take X = 1000).
The name "Doomsday argument" is rather misleading, too. "Doomsday" is usually seen as a bad thing. But what comes after humanity might be the "posthumans" that the people who believe in a technological singularity talk about; is that really doom? Hanson gives a quantitative version of this where there are several "toy universes".
I've talked before about how I'm not entirely comfortable with the "Copernican principle" from which this is derived. For some reason I am much more uncomfortable with this than I would be with the equivalent line of reasoning applied to non-human objects. If I had an urn containing balls labeled from 1 to N, and I didn't know N, and I reached in and grabbed a ball marked 100, I'd say in a heartbeat that the urn probably contained around 200 balls. But the difference is that in the Doomsday Argument we don't even know what the urn is.
The Doomsday argument supposedly only is provisional, until such time as we have better knowledge on how long societies tend to last. This is in my mind one of the most useful reasons for trying to find extraterrestrial intelligence; the knowledge that they do exist (or even a thorough search which doesn't turn up anything) would give us substantial information about how long we might expect to last.
When I studied biochemistry I thought something similar. Essentially all known life forms on Earth have similar biochemistry, because we all evolved from the same ancestors. So an introductory biochemistry class essentially consists of the memorization of those mechanisms. What I would have wanted to see is, say, a dozen or so independently evolved biochemistries, and then see which features of our own biochemistry are just accidents of evolution and which are essential to having complex, self-replicating systems.