Can a planet have a larger diameter than Jupiter? I have heard it said that if mass were added to Jupiter, then only its mass and density would increase but the diameter would stay about the same. Is this the case for Jupiter or some property of Jupiter specifically, or is 150,000 km pretty much the largest diameter that a non-fusing object can achieve?
I am specifically interested in the case of a physically larger object (planet) orbiting a smaller but more massive object (star).
 A: You can definitely get bigger, but not by much. My very vague brain-only recollection is that you can get about half again as wide as Jupiter before things start shrinking again. Source: An article in Scientific American I think, over a decade ago at least; I don't recall any details on when. The article also had quite a bit about brown dwarfs.

Addendum 2012-06-19: It looks like the margin was slimmer than I thought! My quick reading of the excellent references from the other answer is that Jupiter comes pretty close to the maximum radius for a realistic H-He mix gas giant.
I couldn't find the exact quote about sizes for which I was looking in the Scientific American article that I give a link to in my comment on the other answer. I don't know if it was a different article, or if the quote just got deleted when the author updated it.
A: Wikipedia's page about gas giants says so. The paper where the computations are done is arXiv:0707.2895. I haven't read the paper in detail, but the figure you are interested in is figure 4 (p21), where you can see that the maximal size for a planet is roughly 1.5 Jupiter radius, for a planet made of 2000 $M_\oplus$ if hydrogen. 
Beyond this mass, the pressure augmentation at the centre is enough to shrink the metallic hydrogen inside the star and increases the density enough in order to reduce the global size.
Edited after reading the paper: If you want to read only a part of the paper, read §4.1.1. which details a lot of things without being too technical. The computations are made at 0 temperature, and they postulate that the extra-solar planets (slightly) above the H-curve in fig. 4 are due to thermal effect. Also of interest is the fact that they stopped their calculations at 4000 $M_\oplus$ (13 M_J), because deuterium fusion is ignited above this mass, transforming the planet into a brown dwarf. However, Wikipedia says that brown dwarfs radii is approximately constant, so I guess that the thermal affect are still small for them.
