A friend of mine asked me to recommend a point-and-shoot camera. I admit I am biased when it comes to photography things. Photography is not an exact science, so there is no "best this" or "best that".
I believe that all digital cameras these days are capable enough for normal shooting, so the choice is not about getting a "good" (i.e. capable) camera. A very basic entry-level point-and-shoot should be able to shoot without any annoying shutter lag, can expose accurately, and can focus without a fuss.
To cut to the chase, I would be very happy to carry with me the very basic Canon Powershot A1200 on any holiday trip. It costs ~AUD$100. It has a traditional camera grip body to make room for two AA batteries, hence it is not super thin. This type of camera body is much better for handheld shooting than a thin 1cm-2cm body. It has a 1/2.3" sensor that shoots12 megapixel. It has 4x optical zoom, with a decent 28mm wide lens and F/2.8 maximum aperture.The LCD screen is 2.7", 230,000 pixels; certainly adequate. It shoots 1280x720 Mepg4 video with mono sound. The specs are definitely good enough, if not good.
If size is important and you want your camera to be as small as possible, the Canon Powershot A2200 is a good choice. It is a close sibling of the A1200 and has almost identical specs. It costs AUD$96 at The Good Guys.
For something higher up in specs, but with same portability, the Canon Ixus 220 can be acquired for AUD$198 at Harvey Norman. The sensor size is the same, but the newer BSI-CMOS sensor is supposedly 60% better in reducing noise at high ISO. It records full HD video with stereo sound, shoots at up to 8fps, and has wider lens; 24mm instead of 28mm. It can also shoot slow motion video and has a few other shooting effects to whet your palate for creative photography.
In my opinion, most people do not need anything more than the above unless you have an interest in photography as a hobby. Features like super high speed shooting at up to 100fps (Casio) is not something you do all the time. Sweeping panorama (Sony) are not something you would print together with the rest of your holiday snaps. HDR, done well, looks impressive, but they are not what you would shoot at a social event. Somebody is always coming up with something new, but the needs of basic photography hasn't really changed much. Good composition, good exposure, capturing the mood, etc...... you don't need to bust your piggy bank for that.