I received this email today. I was curious of the authenticity of the email and the numbers affected and, after some digging, learned that it is, indeed, real (LinkedIn Blog: Taking Steps to Protect Our Members):

We recently became aware that some LinkedIn passwords were compromised and posted on a hacker website. We immediately launched an investigation and we have reason to believe that your password was included in the post.

To the best of our knowledge, no email logins associated with the passwords have been published, nor have we received any verified reports of unauthorized access to any member’s account as a result of this event. While a small subset of the passwords was decoded and published, we do not believe yours was among them.

The security of your account is very important to us at LinkedIn. As a precaution, we disabled your password, and advise you to take the following steps to reset it. If you reset your password in the last two days, there is no need for further action.

1. Type www.linkedin.com/settings directly into your browser

2. Type in your email address and press Sign In, no password necessary
 3. Follow the on-screen directions to reset your password

Note: Do not reuse your old password when creating your new password.
 If you have been using your old LinkedIn password on other sites, we recommend that you change those passwords too. We appreciate your immediate attention to resetting your password and apologize for the inconvenience.

Thank you,
 The LinkedIn Team