Edit: Since this answer still seems to be generating a bit of interest, let me steer you all towards password_hash() which is essentially a wrapper around crypt() but much simpler to use. If you're using PHP<5.5 there is password_compat which was written by the same guy and is actually linked off of the official documentation.
If you're already using crypt() it's worth noting that both password_verify() and password_needs_rehash() will work with all crypt()-style passwords, so there's hardly a reason not to update!
Use crypt(), it provides MUCH stronger hashing methods.
Hash a new password:
// generate a 16-character salt string
$salt = substr(str_replace('+','.',base64_encode(md5(mt_rand(), true))),0,16);
// how many times the string will be hashed
$rounds = 10000;
// pass in the password, the number of rounds, and the salt
// $5$ specifies SHA256-CRYPT, use $6$ if you really want SHA512
echo crypt('password123', sprintf('$5$rounds=%d$%s$', $rounds, $salt));
// output: $5$rounds=10000$3ES3C7XZpT7WQIuC$BEKSvZv./Y3b4ZyWLqq4BfIJzVHQweHqGBukFmo5MI8
Compare an existing password:
// the hash stored for the user
$given_hash = '$5$rounds=10000$3ES3C7XZpT7WQIuC$BEKSvZv./Y3b4ZyWLqq4BfIJzVHQweHqGBukFmo5MI8';
$test_pw = 'password123';
// extract the hashing method, number of rounds, and salt from the stored hash
// and hash the password string accordingly
$parts = explode('$', $given_hash);
$test_hash = crypt($test_pw, sprintf('$%s$%s$%s$', $parts[1], $parts[2], $parts[3]));
// compare
echo $given_hash . "\n" . $test_hash . "\n" . var_export($given_hash === $test_hash, true);
/* output:
$5$rounds=10000$3ES3C7XZpT7WQIuC$BEKSvZv./Y3b4ZyWLqq4BfIJzVHQweHqGBukFmo5MI8
$5$rounds=10000$3ES3C7XZpT7WQIuC$BEKSvZv./Y3b4ZyWLqq4BfIJzVHQweHqGBukFmo5MI8
true */
