Sometimes, I believe it is just a fad: wide-open lens to shoot creamy blurred background. I like it but I am not too much into it. As it has been said, often a blurred background compensates for the lack of composition skills: what to do with what is behind the subject?
However, a blurred background can also serve a more technical necessity. I needed to have open books in the background, but I did not want them to be readable (commercial stock photography). I managed to get the hands in nice focus and the text fuzzy just as I wanted without editing, just using the Fujinon XF 35mm wide open at f/1.4. Very nice performance of this lens that, despite the small sensor format, gave me a good three-dimensionality and the plane separation that I desired. The close-up shows it well.
Because I shot RAW, I took care of only applying, selectively, sharpening on the areas of the image that were in focus. With Lightroom or Capture One, this is easily done with painted-in layers during RAW conversion. In this case I wanted to use the classic chrome picture style and so I resorted to Fuji’s own RAW converted, generating two final TIFF images–one with sharpening applied, the other one without any sharpening. Then in Photoshop I selectively chose which image layer to use to make the final picture.