I think Sébastien's answer is as good as it gets. But then again to really know if your camera has captured the highest resolution possible, you should use it on a sturdy tripod (or something where you can depend on that camera-shake is completely outnumbered). Do not rely on image stabilizers here. In fact: switch them off if possible! (Use it for all cameras that you compare in the test; thus gaining continuity).
I prefer to use natural textures for these kind of 'tests': grass, mountain-walls, trees, leaf, etc... Nature has an infinite amount of details! No test-card can compare to that.
As in resolving power, do not underestimate the importance of the right exposure: underexposure will lead to loss of detail (and obviously overexposure!).
Also, be careful with compression, because sometimes details get lost where you do not expect at first glance, mostly (colour-)textures (eyes, skin, fur, leaf, wood). When they disappear, the photo gets an unnatural appearance.
I would like to point out to Chris that some cameras do let you choose the compression factor (as in low, mid and high compression), next to the resolution (of the JPEGs that is).
Keep in mind that while taking the photo and while post-processing details can get lost.
Finally, I choose the resolution - in post, I always shoot RAW - that suits the result (1280 pixels max. for web, full resolution for print), regardless of the real resolution as a result of lens quality for instance.
But perhaps that is a way of thinking, because in the past I was unable to change the film size afterwards...