Welcome to Android Central! For files, you can try this method for recovery:
http://forums.androidcentral.com/ge...de-accessing-locked-phone-cracked-screen.html
Unfortunately, this won't help you retrieve contacts stored on the phone, since you can't access the database file they're stored in. This is why it's always safer to associate your contacts with your Google account, not the Phone account. Contacts in the Google account get synced automatically to your Google Contacts in the cloud, where they remain safe.
SMS messages present the same problem--they aren't in a discrete file that you can move over. If this information is very important to you, you may have to consider replacing the screen of the phone instead.