Focus and blur have a reason in a picture when they come together. Blur alone is just a loss of an important element in the photography art, unless it has a reason, like obscuring nudity or creating an additional value... but what is the value of an entirely blurred picture?
Shooting blurred photos can be considered opposite of black and white photography - while black and white is about hiding colors to bring out shapes and shadows, blurring helps to reveal colors by hiding shapes and shadows. An interesting subcategory is a combination of the opposites - black and white blurs - where distractions by both details and colors are hidden away to bring out larger shapes or patterns.
Blurred images could be used for several purposes, like
- to hide boring shapes that have interesting colors;
- to hide unwanted details on interesting shapes;
- to give feeling of mind-boggling motion;
- to evoke memories - colors/shapes alone can trigger some memories stronger than same image with details - because only the colors/shapes match memories of other people, not the details;
- to initiate curiosity - a blurred image and a catchy title might induce a person into taking some action, like reading accompanying article;
- to differ from the ubiquitous super-sharp photography;
- to suggest a hurried "caught moment";
- to suggest that someone is leaving (walked out of focus);
- to create some new shapes with light sources leaving stripes in the frame.
As an example, Michael Orton is a photographer who has taken lots of great blurred images. The roots of creating blurry images are, however, much older, starting with (pre-)impressionist painters like Joseph Mallord William Turner (aka "the painter of light") and Claude Monet.
One more suggestion: if the picture is meant to be a background for something else (like a computer desktop, a printed page or a work of art), then the "something else" forms the foreground of the resulting work, and the picture in the background should not excessively distract the viewer from it. Thus, a completely blurred or defocused picture may be exactly what the overall composition needs.
It's also worth noting that not all blur is the same: for example, motion blur only loses detail along the direction of motion, but retains variations orthogonal to it. Besides, blurring can also add detail. For example, a defocused photo can show the camera's bokeh, while motion blur adds information about the movement of the subject (and/or the camera). An extreme example would be star trail photography, where the motion blur is provided by the Earth's rotation. Obviously, these images are blurred by definition — but that blur is precisely the subject of the image.