Which point and shoot cameras support RAW images? Is there any way to take RAW images on unsupported cameras?
Many Canon PowerShots can, using the alternative firmware CHDK (found here: http://chdk.wikia.com/wiki/CHDK)
Arguably, no point and shoot camera can shoot RAW, because if it could, it would cease to meet the definition of a simple camera you just point and shoot and get automatic acceptable results. I know that many people use "point and shoot" to refer to any small camera despite that argument, but the point is important. Since the term can mean a lot of things to a lot of people, you have to decide what aspect of what you are referring to is the part you're interested in — because the right answer depends on that.
A, B, and C below refer to three possible interpretations of "point and shoot", along with why one might want RAW from that kind of camera, followed by suggestions on how to find what you need.
A. I would like a cheap camera but want better quality or flexibility out of it.
In this case, a Canon camera with the CHDK alternative firmware is the best bet — you're really not going to beat that.
B. I want a compact camera with advanced features and I'm happy to both pay for and work for better results.
Here, you have several options depending on your need. There's an emerging — or re-emerging, since it parallels market options like the Olympus C-5050 from a decade ago — segment which DPReview calls "enthusiast compact". These can work like a point and shoot in many ways, but they're aimed at the non point-and-shoot photographer. The link there goes to a round-up from a year ago, and the specific models will change, but basically everyone has got one. This link from Neocamera showing compact cameras with RAW output basically covers this category, or similar from DPReview.
→ Update: in December 2011, DPReview ran an article entitled Buyer's Guide: Enthusiast raw-shooting compact cameras, covering exactly this category, even more specifically than last year's roundup.
Or, depending on how important small and cheap are vs. flexibility, you may be interested in a mirrorless interchangeable lens system camera, like the Micro Four Thirds offerings from Panasonic/Olympus, Sony NEX, or Nikon 1 — or even Pentax's ultra-tiny Q.
There's also a few unique cameras like the Fujifilm X100, which isn't really compact or a point and shoot, but also isn't a DSLR.
C. I do want automatic great photographs by just pointing and shooting, and I've heard that RAW is better than JPEG, so I want a camera that can do that.
In this case, you should rethink your assumptions.
No, not all point and shoots can do RAW. Check your camera's manual to find out if yours can. If buying a new one, check the features list. Usually only the more expensive ones have RAW shooting facility unfortunately. Cheap ones tend not to have the feature.
I have the utterly excellent Canon PowerShot S95 which can shoot RAW. I love it. :-)
Panasonic DMC-LX5 and the Leica clone of it allow for raw format. However, the easiest way to see this is to visit a site, like DP Review that has a database of this information. The link there will take you to a list of 39 that support the raw option. :)