I posted this tip a little over a year ago when Lightroom 3 came out, but I thought I’d post it again, since surprisingly it is one of my most-read posts.
Looking to blur out a background to reduce distractions? In Lightroom 3 or later, use the adjustment brush with Sharpness at -50 to -100. If this is not enough blur, do it again: click on New to start a new adjustment, and paint a second time. If you blur out an object that you want to keep sharp, use the adjustment brush and paint back over the object with +100 Sharpness to restore its sharpness!
Also consider using the graduated filter with -100 Sharpness to simulate a shallower depth of field where the sharpness drops off gradually.
If you don’t know how to use the adjustment brush, here is an old video on it (that for better or worse requires that you have flash to play it). It is a sample video from my Lightroom 3 DVD, but everything covered is also applicable to Lightroom 4, 5, 6 and CC (these newer versions of Lightroom do have additional features in the adjustment brush).
The adjustment brush, graduated filter and radial filter are covered in-depth in my Lightroom CC/6 and 5: The Fundamentals & Beyond video series (and earlier versions).