The Micro Four Thirds system is not ideal for getting thin DOF. To get a thin DOF, you are better off buying a camera with a large sensor, for example full frame DSLR cameras.
However, it is still possible to get a thin DOF with Micro Four Thirds if you use a close focusing distance. I have evaluated the out of focus rendering (bokeh) at close focus using three lenses: The Lumix G 14mm f/2.5 pancake, the Lumix G 20mm f/1.7 pancake and the Lumix G 14-42mm f/3.5-5.6 kit zoom lens.
I took the same picture using the three lenses at various apertures. Here are the full images at maximum aperture:
Lumix G 14mm @ f/2.5
Lumix G 20mm @ f/1.7
Lumix G 14-42mm @ 14mm f/3.5
Lumix G 14-42mm @ 20mm f/4.1
The focus was set on the emblem on the bell in the middle left part of the image. I used the Panasonic GH2 at base ISO, and the shutter speed was around 1-6 seconds. I used a tripod, and also two second shutter delay, to avoid camera shake.
The images above are taken using the maximum aperture available with the given lens. Hence, the DOF is as thin as possible, given the focal length and focus distance.
To better evaluate the bokeh, I have made 100% crops from two parts of the image (click to enlarge):
The first crops are from the focus area. From these images, it could look like the 14mm pancake lens is unsharp. However, these images were taken primarily to evaluate the bokeh, not the sharpness, and the focus point might be slightly different between the lenses. In my experience, the sharpness of the 14mm pancake lens is rather good.
In the seconds image, we see the out of focus highlights. I suppose one could say that neither of the lenses give a very nice bokeh. They have various problems. They all exhibit some ringing, but it seems to be worst at 14mm. Also, the bokeh is uneven, and "dirty", "swirly".
The 20mm pancake lens shows the most non-circular highlights, both wide open and closed down.
The 14-42mm lens shows some strange irregularity at f/5.6, at both 14mm and 20mm. This could look like a construction error of the aperture diaphragm. However, it is not likely to pose much of a problem, since only at very close focus distance would you see much out of focus rendering at f/5.6
In terms of roundness, the 14mm pancake has the most consistent appearance.