One quick tip if you're using the flash on a P&S is to use something to diffuse the flash. Simply hold a piece of white paper or thin plastic or something similar in front of the flash and you'll almost always get better results.

In a "normal" room (i.e., a room of normal ceiling height), using the ceiling is a solid bet. If your camera has TTL flash metering (and which self-respecting DSLR doesn't?) that'll help you take "perfect" pictures, every time.

(Note: "perfect" means people will ask you how you did it, and be suitably impressed at your photography skizzles)

Firing flash along the axis of the lens is a poor idea almost always. Also, your pop-up flash has an effective range of ~10 feet (depending on camera), so popping it beyond that range (which I see many people do) is basically pointless. In fact, if there are objects near, what the camera will do is expose for those objects, leaving your main subjects, who are too far away, in shadow.

This is why you'll see those crazy pictures where everyone is real dark and has glowing eyes.

But all in all, the solution is to get a faster lens - there are many point and shoots that have premium, fast lenses. Going for those will allow you to skip the flash for a lot more occasions, making better pictures overall.