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Blurred photos are popular enough that there are even special lenses made specifically to get this effect - the Lensbaby series. A Lensbaby puts one area of the photo in sharp focus and diffuses the rest of the picture, drawing attention to one spot.
Of course, photographers were experimenting with these techniques long before special lenses were available. Simply smearing Vaseline on your lens filter can give much the same effect. (Note: if you try this, be sure to put the Vaseline on a cheap filter, NOT directly on the lens!)

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Naturally, the effects can be simulated in Photoshop as well, although many photographers believe they get better results using hardware. The photo to the right was taken with a regular lens, then modified using Photoshop to get an exaggerated Lensbaby effect.