As good a picture? Depends. Any of the compact small-sensor cameras can shoot fine pictures at low ISO settings. Some of them allow shooting raw files, so you get the advantages of post processing your own, if you prefer that. Even the JPEG files from my G-7 are fine at ISO 100. By ISO 200 they are not so great, and at ISO 400 they look pretty bad. If you want great image quality at high ISO values, bring your DSLR.

The advantages of the compact P+S camera are: size, weight, and, uh, weight. Bring a spare battery and shoot for a week. The disadvantages are image quality, speed, focus, and lack of manual control. If you want a good, small, fully featured camera, take a look at the Panasonic TS2, which is waterproof to 10 meters, has optical image stabilization, a wide angle lens with a decent zoom range, and takes reasonably good photos (again at low ISO settings.)

If you want a compact camera that shoots great files, take a look at the micro 4/3 systems. These have a much larger sensor than the typical P+S camera. I have a Panasonic GF1 with the 20mm f/1.7 lens, and the files are terrific -- easily as good as files from my Canon 40D even at ISO 800 or 1600. The camera itself is about the size of a large-ish point and shoot, and smaller than the "super zoom" models. Everything in this gallery was shot with the GF1 and the 20mm lens.

I bought the GF1 as an "every day carry" camera -- something that would give me high quality images from a small camera. It's compact enough that I'll be using it as a hiking camera, too. The downside to any of these systems is the cost -- they aren't cheap (though if you want to feel better, price a Leica M9 and a couple of lenses. My first house didn't cost that much....)