Is storing the hash of a key together with ciphertext encrypted with that key secure? Is it secure to store the hash of a symmetric cipher key along with data encrypted with that key? Are there any circumstances or algorithms in which this combination could lead to potential weaknesses -- or is it always a bad idea? Assume the cipher is AES-128 or -192 and the hash is SHA-256, and also assume that the key was derived from a pass phrase.
I think this is generally not a good idea, for two reasons.

First, do not generate a key as a hash of a passphrase.  Where possible, you should try to avoid deriving cryptographic keys from passphrases, as passphrases rarely have enough entropy to make a secure crypto key.  If you must derive the crypto key from a passphrase, then be sure to use PBKDF2 (or similar key derivation function), which is specifically designed to mitigate (but not eliminate) some of these risks, by making key derivation a slow process.

Second, if the key is derived from a passphrase, I do not recommend storing a hash of the key.  This may make it easier to mount exhaustive passphrase-search attacks, including facilitating construction of rainbow tables that map from the hashed-key to the original passphrase.  Instead, simply use authenticated encryption.

If you use authenticated encryption, there's no need to store a hash of the key.  You can tell whether a key is correct by trying to decrypt and seeing whether the decryption is authentic.  If it is authentic, you're good; if it isn't authentic, you've got the wrong key.

And you probably want authentication anyway, so this kills two birds with one stone.