I bought this camera because, with the birth of my baby daughter, I wanted a small, pocket camera that is always ready and I can take everywhere, when my big camera feels bulky. If possible, I prefer to shoot RAW, because I generally enhance my photos in Lightroom. And the company I work for provides me with an economic blackberry that has a crappy camera, so I don't have a smartphone that could cover this need.
In that regards, the Sony RX100 brilliantly accomplishes its objective. It's incredibly small for its features. Despite all the functionality it packs, it's very easy to operate (I didn't need to read the manual, unlike that of my Panasonic GH2, which I have to check from time to time). The image quality is amazing due to its sensor size and quality. Despite its 20 megapixel count, noise level at high ISO is incredibly low so, together with its large aperture, you can take more than decent images with available artificial light. The screen is also brilliant (literally).
The finish is so nice that you will want to take it with you everywhere, thus allowing you to take more and better pictures. And I don't understand the complains I read about the charger. Using micro-USB allows for both wall socket or computer charge, and if you already own a smartphone, you will probably share the charger. The only problem could be if you needed a spare battery, but for now I can live without it, as long as I fully charge it if I plan a busy day.
The main caveat, however, is that the maximum aperture drops very fast when you zoom in (the lens is spectacular, but optics have their limits). Therefore, the possibilities for shallow depth-of-field are very limited. Forget about portraits with blurry backgrounds. With f1.8 in close-ups you can get it, but at 28 mm equivalent focal length, if you take a close-up portrait, the face will be distorted (big nose and lips). You will have a blurry background and a ugly, and probably angry, foreground. And at a more flattering focal distance, maximum aperture (around f4.5) is not enough. So don't believe in Sony's promises of blurry background, except for macro (which, by the way, with a minimum distance of 5 cm, is incredible). The f1.8 is great, however, for low-light wide angle (landscape, groups of people) pictures.
The other main concern is the price. It is certainly expensive, but it is unique in its class. You have more economic options, but they are not so good. And there are cameras (DSLR or mirrorless, especially with prime lenses) that, for the same price, will render nicer pictures, but none of them are pocketable. So in the end, the choice is a balance between money availability, size, and image quality, in which you will have to decide what is more important for you.