Note that if you store your passwords in a fast hash format like salted SHA1, an attacker with 32MM database rows can publish a very credible sample of usernames and passwords, and leave you scrambling to explain how the breach isn't really as bad as it looks. Not a great position to be in. The right answers to this problem are BCrypt, SCrypt, PBKDF, or (at a minimum) salted "stretched" SHA1, iterated many thousands…
What's wrong with using a salted hash? Assuming a competent implementation, it should be computationally infeasible to brute-force any digests in less than a few billion years using current models of computation. I'm particularly curious about how using (for example) BCrypt will prevent brute-forcing "12345", "password", or any of the other simple strings many people use.
Because you've been assuming that the database will be breached and that no other kind of attack can happen.