Copying data from unbootable Mac
If you have another computer that can support target disk mode, simply boot with T held and connect per your MacBook (usb or thunderbolt or FireWire are all possible target disk mode). Your Mac is now a hard drive to copy / recover the data. 

If not, Assuming you do not have a current Time Machine Backup then...

If you can boot to the Recovery HD, then attach an external USB/FireWire/Thunderbolt drive (whichever works for you since you didn't state what Mac you have, and boot to Recovery HD and then use Disk Utility to make a Disk Image of your Home Folder to the external drive.  Or a Disk Image of whatever Folders you want to save.

In Disk Utility click, File > New > Disk Image from Folder...

In the Select Folder to Image dialog box navigate to the target location, e.g. /Macintosh HD/Users/$USER and select the Folder, then click the Image button.

In the New Image from Folder dialog box, name the image and then navigate to the external target location to be saved and then click the Save button.

In this example, you now have a disk image of your Home folder on an external drive and can copy your User Data back from that image after you clean install the OS.