I agree with Danny H, but wanted to address the other half of your question too: protecting the login (usually an email address). Most people ignore the need to protect it, but for website that want to maintain secrecy of their customers (not just Ashley Madison but also medical websites), then you'd want to add a layer of protection for the other data.
First, a reference on protecting the password: Secure Salted Password Hashing. Use either bcrypt, scrypt, PBKDF2, or argon2.
Now what about protecting the login? You can actually do a similar thing for protecting it, but you will need a fixed salt for it (for passwords, the salt must not be fixed!). Let's assume bcrypt is used for my example below.
Consider how the user would login: User enters his login id and password. System applies bcrypt to login id with fixed salt to look up user in database. From that, system gets the user's password salt, and system computes bcrypt on user provided password with salt to see if it matches hashed password in database. If so, user is granted access. Therefore, system granted access without storing the user’s login id in plaintext form in the database.
What about user forgetting password? No problem if the login id is the email address: the user enters login (email address) on forgot password page, system applies bcrypt with fixed salt on user entered email address to see if the user exists in database, and assuming yes, then emails the user a secret link for password reset. Within the database, we have to associate that secret link to this user to make sure he only resets his own password (not somebody else’s!).
What if the database is exposed? Anybody could determine if a specific user is in the database by computing bcrypt on that user’s email address and looking for a match in the database, but nobody is going to be able to reverse the entire collection of email addresses, which is a big improvement over the present situation.
I discussed this idea in a blog of mine more than 2 months ago, see: https://littlemaninmyhead.wordpress.com/2015/09/08/a-retrospective-on-ashely-madison-and-the-value-of-threat-modeling/