What prime lenses can you recommend for producing pleasing bokeh on the Micro Four Thirds cameras like the Panasonic GH2/3?
I'm interested in both Panasonic and non-Panasonic lenses (including using adapters).
As mattdm said, the Panasonic Leica Summilux DG 25mm F1.4 produces nice bokeh. Many other lenses such as Olympic 45mm 1.8 can produce good bokeh, you can have a look to this reference.
Any lens with shallow depth-of-field can produce bokeh, but the word pleasing is subjective. Most people like circular bokeh, so a lens with more diaphragm blades produce better bokeh. As you don't mind using an adapter, and manual focus, the Minolta 58mm f/1.2 produces great bokeh for a small budget.
The micro-4/3 format has many excellent prime lenses available. As far as Zuiko lenses go, I recommend the following:
As mentioned in another answer, the Olympus M.Zuiko 75mm F1.8 is a fantastic lens. It is very sharp, and the bokeh is smooth and lovely.
If that focal range is not your style, the Olympus M.Zuiko 45mm F1.8 is a very good substitute. It's great for head/upper body portraits, and the sharpness and bokeh almost match the 75mm. Even better, it's very affordable for the quality you get.
Both of these lenses have very good center-to-edge sharpness.
The Olympus M. Zuiko 17mm F1.8 completes the trinity. Like its siblings, it is a very sharp prime, but at the 34mm equivalent focal range, you are not going to get much bokeh out of it.
Blogger Robin Wong has reviews of these lenses with many accompanying real-world photos:
The one that comes to mind that is superb, is the Olympus 75, which bokeh is very pleasing indeed! Would fit your GH3 as a glove ;-)!