While researching the Sorites/paradox of the heap for snarky, half-funny joke about cannibalism related to the human-hair-soy-sauce story, I discovered this much cooler wikipedia entry about paradox, with plenty of neat examples:

Fermi's Paradox, that the aliens ought to be here already, an old favorite (more here)
The Unexpected Hanging Paradox, so delightfully kafkaesque
The Cretan Liar
Newcomb (Today feels like a "take just the closed box" kind of day, though I could perhaps be persauded otherwise)
The Mere Addition Paradox (I actually kind of got into a version of this other on Matt Yglesias's blog the other day, only with Rawls)
The Raven Paradox (epistemology): does seeing a red apple provide evidence for the hypothesis "All ravens are black"?
The Berry Paradox: What is "the first number not nameable in under ten words"?
Epicurus and the problem of evil
And, of course, Zeno.
And many others.

My favorite one today, though, is Buridan's Ass. How do we make a rational choice between our two beloved sons, both of whom are drowning at just-barely-reachable, equidistant points in different rivers?

Second favorite? Kavka's Toxin. Can you intend to do something you know you'll never have to do?