These are the best compacts for image quality:
Canon G12
Canon S95
Nikon P7000
Olympus XZ-1
Panasonic LX5
Samsung TL500
FYI, most often people get poor photos because they do not know much about photography, or the limitations of small cameras. If you are wanting a compact P & S to capture images of kids playing indoors, no small camera can do that well, not even the more expensive compacts I have listed.
Hi, I'm looking for a compact point & shoot camera with the best image quality possible. I've read a bunch of reviews for various cameras and figured out what I want for features, but at the end of the day the image quality is the thing that matters most. So I want to know which models are the best in that department - price is not an issue.

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GameFAQs
GameSpot
Giant Bomb
TechRepublic