I agree with the earlier post about the Olympus with the slide cover. They are difficult to use and can be frustrating. The higher end Olympus' do not have this problem and are very nice cameras. My biggest gripe with them is that they do not offer image stabilization on their ultra zooms. I really think that they have the best image quality, but I do not want to carry around a tripod to use my zoom.
I am on my second Canon (A70 and now S1 IS) and I am very happy with it. I looked at the Fuji 5100, but it did not even come close to the S1 IS even though it is a little cheaper. In my opinion, the 5100 is not even usable at wide angle due to the vignetting.
If I was going to get something with a small zoom (3x - 6x) and was just considering quality, then I would look to Canon, Panasonic, Olympus, or Sony. HP, Kodak, and Fuji seem to only be concerned with marketing instead of features/quality. I am not saying that you can not take incredible pictures with those brands, but sometimes you do not realize what you are missing. Go and try out the ones that you are considering in a camera store. Avoid the big stores like
Best Buy because they never give you any useful help. You have to chase one of them down just to get a memory card to test with. I always tell everyone that asks my advise. Look at them in person and buy the one you liked the most.