While all of the information above is accurate, it's basically only useful for spotting people who are either uncomfortable with a weapon or who are carrying it improperly. Most quality holsters that are designed to be concealed are very difficult to spot, and the people using them are used to carrying, and won't display the behavior and obvious tells shown above.

The people who do carry pistols regularly are usually either 1) a licensed concealed carry permit holder and/or 2) off-duty police, military, or security personnel. These people have, to a greater or lesser extent, a good reason to have a weapon.

Other people carrying a concealed weapon are usually doing so illegally, and won't have the training or common sense to properly secure their weapon. If you see any of the above behavior, it's a good idea to get out of that situation. Drawing attention to the fact isn't a good idea, because either you're revealing that knowledge to a criminal, OR you're implicitly accusing a legal weapon holder of doing his or her job improperly. If the person carrying is so negligent that you can actually see a gun with your eyes, alert the police: if they intervene, they'll either be arresting someone who is carrying a weapon illegally, or giving a legal permit-holder a strict talking-to (or even revoking their permit) for not doing enough to hide their weapon.

There's a third category: people who are carrying handguns openly (i.e. in a holster outside their pants or shirt) without a uniform or other obvious reason for doing so. In most places (but not all) this is illegal. Before alerting local police, make sure you're in a state or municipality where this is in fact a crime - sometimes even the police aren't sure exactly where it's legal to carry a weapon openly, thanks to overlapping state and local laws. When I lived in Colorado, where openly carrying a handgun is legal for most adults, I only ever saw off-duty police exercise that right. It's something of a headache. If you know you're in a state where open-carry is illegal, and you see someone openly carrying a handgun without any obvious police, military, or security markings, call the cops immediately.

Addendum: rifles and shotguns are different than handguns, and are treated differently under the law. Seeing a civilian walk into a public building with a rifle is obviously cause for immediate alarm. But seeing a rifle case in the back of a pickup truck with a dead deer in the bed probably isn't. Again, it's a good idea to use common sense and know your local gun laws.

This information is presented with United States residents in mind. Your mileage may vary, even in the US. This site has a good state-by-state breakdown of what's permitted and where. http://www.handgunlaw.us/