Now that we've had such fun with the Sony RX100, it's time to think again about cameras. I was literally blown away by the quality of the RX100. It is to be sure a pretty amazing pocket camera and in good light has great resolution (F/3.2, ISO 125, 10.2mm focal length with RAW, it has incredible resolution (2600 lw/ph center, 2400 lw/ph edge for MTF-50 or 10MP effective!). As Scott says a key variable is the quality of the lense and then for really high resolution, how good the anti-shake technology is since handheld, it makes a huge difference. The RX100 Mark II fixes a bunch of things that were issues (like a grip, having a filter assembly)
I found two surprising things while using the camera: a) The screen really doesn't work well in the bright sunlight. Either you guess what you are shooting or you get a lense magnifier like the Clearviewer and b) I used the wide angle at F/1.8 way more than I thought I would and when you need to zoom, with so many pixels, it is pretty easy to just crop. The other things I expected: c) low light performance is just OK compared with a big dSLR but most of the time you don't need a flash and d) it is super hard to setup because the default controls just don't work, but the web fixes that with some great recommendations and e) it does take super video with its contrast detection.
Scott recommends getting two cameras and I'll add a few more to consider. As a reference, the incredible Sony RX-1 (full frame F/2 at $3K delivers 2850 lw/ph at center and 2610 at edger a 12MP equivalent) while the Sony DSC-RX100, a 1" sensor does best at 10.4mm focal length (wide open) at F/3.2 at ISO 100 of 2450 lw/ph center and 2300 lw/ph edge or 8.7MP equivalent. This shows that in a real camera, the very best is about a third more resolution than a "point and shoot". the RX100 is not a bad camera at all (*although other test shows max resolution at F/5.6): • Ricoh GR. This is a fixed lense F/2.8 28mm equivalent, so its a big change, but the picture quality is incredible. It is an APS-C sensor and doesn't have an anti-aliasing filter so it is super sharp.$900 from Amazon. The other options in this category are the more expensive but about the same performance Nikon Coolpix A and the bigger.
• Fuji X100S. This has the look of a rangefinder (retro-style) and has its adherents (eg Bob, Luminous-Landscape and Ken Rockwell). It's the geeks choice with its X-Trans sensor and it has a real hybrid viewfinder. It's big issue is OK AF (used to be not so good). They love the image quality mainly and the fact that in camera JPEGs are as good as the RAW output.This is a "big" camera at 445g (nearly a pound). And the lense is 23mm F/2. Technically Photoreview.com.au says it has a max resolution of 2675 lw/ph center, 2275 lw/ph edge at f/4 at ISO 200. It's JPEG is within 50 lw/ph of RAW so that's pretty amazing. 10 MP effective)
• Fuji X100S with its hybrid viewfinder, 35mm equivalent F2 lens and its X-Trans sensor but is over a pound (vs 8 ounces) and much larger. It is 126x74x54mm vs the GR's 111x64x40. This is my buddy Bob's choice. At F/4, Photoreview.com.au shows it's peak resolution at F/4 of 2700 lw/ph (?!!!) and edge is at 2250. Pretty amazing in both raw and jpg. They also did a Imatest by ISO and found that Raw adds quite a bit more at ISO 800 and above (2700 lw/ph vs 2550 lw/ph) and that the peak resolution is ISO 200. This works out to a 10MP equivalent image (with a 75% center and 25% edge weighting to give some sense of softness). A
• Olympus OM-D E-M5 or the Olympus EM1. The upcoming replacement for the Olympus MD5. Rennie was right, the Micro-4/3 does strike an incredible balance of size and lense quality. They dont have too many zoom lenses though which is sad. With the kit 12-50mm F/3.5-6.3 which (in RAW) delivers 2900 lw/ph center at ISO 200 and 2600 at edge which is a 12MP equivalent. Pretty incredible with a kit lense
• Sony in 2014. This is his dSLR body replacment although I'm also tempted to wait to see what Sony does in 1Q2014 as they are rumored to be doing a full frame camera that is an ILC.
• Canon EOS 100D. If I don't feel like selling my  worth of Canon lenses, here is their easy upgrade with 18MP and it is light 370 grams (body only) and is about the same size as the OM-D E-M5. With the kit lenses EF-S18-55mm F/3.5-5.6, it has similar performance to the EOS 700D. And delivers 2750 lw/ph center and 2650 lw/ph edge or 11MP. So with an APS-C sensor less than the Olympus but probably not noticeable at 11MP. It's main issue is less dynamic range than comparable cameras, so you have to turn on Highlight Tone Priority to get it back which actually takes the photo at -1 EV (that is an ISO 200 shot is really ISO 100) and then digitally increases the gain which works well in good light (since there is little noise in the shadows, turn it off in a dark exposure).

issue is AF at night.

• Nikon CoolPix A. This is almost the same camera as the Ricoh (both based on the same Sony sensor).

Getting technical for a moment, if you remember, the Sony RX100 is about 2200 lw/ph (line widths per picture height) which is about a 7MP equivalent at the center and when you are at F/5.6. This is pretty incredibly good. The Sony is about 2200 lw/ph at F/5.6 so about the same.
The Ricoh is similar with less fall off at the edges and it is excellent wide open at F/2.8 according to Imatest:

Even shooting wide open, the Ricoh GR is one of the sharpest cameras we've tested. At f/2.8, the center of the image is about 20% sharper than the extreme borders and corners, but stopping down to f/4 or f/5.6 narrows the gap to just 10% or so. At every aperture down to f/11 (where diffraction really begins to kick in) the GR resolved an average of at least 1900 lw/ph at MTF50 across the frame, peaking as high as 2160 lw/ph.

Accessory-wise, here are what some folks are saying:

I use an external viewfinder, the kind that slips into the flash hot shoe. Ricoh makes a great one, I'm sure. However, I got one from a popular online auction site at a fraction of the cost. The quality probably isn't as good and for this application it works just fine.
Amazon.com: Customer Reviews: Ricoh GR 16.2 MP Digital Camera with 3.0-Inch LED Backlit (Black)

A couple accessories I've found very handy are the OP/TECH USA Bin/Op Strap and the Wasabi Power Battery and Charger Kit for Ricoh.... The neck strap connects easily to the camera, doesn't allow the camera to slide around when it's on my neck, and supports my goal of quick access. The batteries fit perfectly and last as long as the "official" one that came with the camera. Besides, Ricoh doesn't provide an external charger with the camera and this allows you to shoot *and* charge at the same time. Amazon.com: Customer Reviews: Ricoh GR 16.2 MP Digital Camera with 3.0-Inch LED Backlit (Black)