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.
I've also seen a fair bit of misunderstanding about hashes - you do not want to apply a global salt to all your hashes. Salts should be generated on a per hash basis, and should be stored within the hash itself. Most hashing libraries will do this. It's usually much easier and safer to use a library than to roll your own.