Many times data can be recovered for free by:
1) moving the malfunctioning drive into another computer bay and then transferring files/folders.
2) moving the malfunctioning drive into an external drive enclosure and then transferring files/folders

If the above methods fail there are:
1) companies that sell software to repair drives
2) companies that are in the business of data recovery.

These were some on the first page of a google search:

How To Recover Data After Hard Drive Crash

Hard Drive Recovery Tips - How to Recover Data from a Dead Hard Drive

Failed Hard Drive Data recovery - [Solved] - Storage

How to Recover a Dead Hard Disk: 9 Steps (with Pictures) - wikiHow