A normal f/5.6 kit lens on a cropped sensor camera (in this case, equivalent to 84mm f/11) generally is not able to blur the background well for portraits:
A lens equivalent to 100mm f/4 on a full frame camera such as the Olympus ZD 50mm f/2.0 2x crop lens is much better:
This one is taken at f/4 (ie. equivalent to 100mm f/8 on full frame):
And this lens wide open at f/2.0 (ie. equivalent to 100mm f/4 on full frame) becomes a very nice portrait lens:
While a lens equivalent to 170mm f/2.8 such as either a Canon 135mm f/2.0 on a 1.3x crop camera (as shown here) or a Rokinon 85mm f/1.4 lens on a 2x crop camera will give much shallower DOF and allow more background blurring:
NOTE: in the above images, subject magnification has been maintained constant, but the change in effective focal length while not altering DOF (this was achieved by altering effective aperture), has meant the camera must be further from the subject, and the background becomes more compressed (“perspective” is altered) as the effective focal length is increased.