Company’s Blog: “In our investigation, we have found no evidence that encrypted user vault data was taken, nor that LastPass user accounts were accessed.” Nonetheless account email addresses, password reminders, server per user salts, and authentication hashes were compromised.
Because of that everyone using the LastPass service will receive a mail, prompting them to reset their master password, according to the blog entry. On top of that the company will also require users who log in from a new device or IP address to verify their ID via mail if multifactor authentication is not enabled for the specific account.
Considering your stored passwords the blog says: “Because encrypted user data was not taken, you do not need to change your passwords on sites stored in your LastPass vault. As always, we also recommend enabling multifactor authentication for added protection for your LastPass account.”
So apparently there is no need to change every password you have stored with them. You can if you are really really concered for your accounts, but according to LastPass there is no need for it. Just make sure none of the other passwords you use is the same as the master password of your LastPass account.