This is a pretty basic phishing scam, the email or message or website will ask you to provide your email address and the password to access that email account.  With this information, they can review all of the emails that you have sent or received, reset passwords and access emails on other online services, such as credit cards, bank accounts, cell phone accounts, mortgages, 401(k)s, and any host of online services.

Facebook even attempts this type of phishing activity.  This last week, it was reported that "Facebook has been demanding some new users enter their email passwords in order to sign up for an account on the site."  This is classic bad software design and most probably phishing.  When the user signed in their email password, Facebook would attempt to connect them with everyone in their email contacts list as a Facebook Friend.  Very shady practice.