Recover data off internal memory of a pin-locked phone? How to retrieve data off of internal memory for LG Optimus (android 2.3.4), not rooted, locked via PIN password, and no forgot password showing up on PIN entry screen?  I'm more particularly interested in contact data then anything else.
Using adb, you can use adb pull to take any file you want from your phone, event if it is protected and locked (I tried on 4.1.2, don't know if it works on more up to date versions).

Only the /data folder needs root privileges to be read and it is where your contacts are stored. If you have root privileges, you can look at this answer to know where you can find them.

Note that you have to enable USB debugging before trying these steps.