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 a video on it. It is a sample video from my Lightroom 3 DVD, but it is equally applicable to Lightroom 4.