The two most common methods, md5 and sha-1 are both susceptible to collisions, or birthday attacks. As of writing this, I would recommend using SHA-3-256

The two most common methods, md5 and sha-1 are both susceptible to collisions, or birthday attacks. As of writing this, I would recommend using SHA-3-256 which has no known attacks. Don't do that. Hashing algorithms without salt and iteration counts is a bad idea. Thankfully, languages and frameworks are starting to take this responsibility away from the programmer (or at least they're making it easier) – consider using has_secure_password in Rails, password_hash in PHP 5.5, etc. Don't use standard hashing algorithms.