It's more secure against dictionary attacks and rainbow tables, anyone that tells you otherwise is a grade A ****ing idiot.
It makes it weaker to collisions though.
People that go on about 'oh double hashing doesn't improve security' really need to have their ability to talk taken away.
Here's a quick example; If a hashing mechanism outputs a 32 character code from any input, and for A you run it once and B you run it twice:
A can be found in a lookup table expecially if it's less than 13 characters. A can also be found using a dictionary or brute-force attack.
B will not be found in a lookup table because it's 32 characters. If someone can provide even a 16 character rainbow table for MD5 (which is known to be broken) please, do. B will not be found in a dictionary attack _AT ALL_ and is incredibly unlikely to be found via a bruteforce attack UNLESS a collision is found. If a collision is found, they have an alternative string that hashes to give the correct MD5 hash, they can't they crack that string to get the original data used for the first MD5 though.
The real problems are, if someone has access to your site and database whereby they can read off all the hashed passwords, they can change any password to login to any account so don't need to crack the password at all, if however they want to get something else like a bank account or email account and the person has used the same password for both sites, that's what they'd be cracking the password for.