What can a person do with special private keys? The Alert message in the Standard Client will only be displayed if it is signed with a correct ECDSA private key. Should anyone get that private key, they would be able to propagate any alert through the Bitcoin network, possibly causing some harm.

What can a person achieve with special private keys in regards to the Standard Client and anything directly related to it, and moreover, what public key / address are known to correspond to such keys? (For example, a preferable answer would be "With key X and Y one can do Z")
As far as I know, the alert key is the only special one with a public key hardcoded in the client.

Technically, the public key of the genesis block's output is also hardcoded in the client, but it grants no special privileges. The genesis block cannot even be spent.