What is a compressed Bitcoin key? The standard Bitcoin client in version 0.6 apparently introduces compressed keys.

What are they? Are there any drawbacks to using them? Any incompatibilities with older software? Reductions in cryptographic strength?
A compressed key is just a way of storing a public key in fewer bytes (33 instead of 65). There are no compatibility or security issues because they are precisely the same keys, just stored in a different way. The original Bitcoin software didn't use compressed keys only because their use was poorly documented in OpenSSL. They have no disadvantages other than that a little bit of additional computation is needed before they can be used to validate a signature.

If you think of a public key as a point somewhere along a giant letter U, an uncompressed key is the x and y coordinates of the point. A compressed key is how high up on the U the point is along with a single bit indicating whether it's on the left or right side. As you can visualize, they both encode precisely the same thing, but the compressed form requires half as much space plus one bit. (Of course, they're really points on elliptic curve secp256k1, but the concept is the same.)