Backing Up Hard Drives To External, Important Data I.e Pictures Music

I have always backed my personal hard drives using images for easy restoration

However i now have 2 PCs that need backup performed and they just want the data so an image is not necessary thus i only want the important data ie; documents and settings important files no junk such as updates or temp files

I would prefer to remove the hard drives and plug it into another pc to perform the backup instead of doing the back up from the actual machine