Using weather sealed camera bodies and lenses helps, but each condition has its own issues.

• Rain: in light rain you can probably get away without doing anything special, but in heavy rain, you'll need to wrap your camera in a plastic bag with an opening for the lens. Dry it off well with a towel when you get inside.
• Heat: Two separate issues... static and air conditioning. In very dry climates (like the desert) you can have static buildup. If you are using film, you might experience triboluminescent sparks which will partially expose the film. Wind slowly. Also when going in or out of air conditioning keep the lens cap on until the camera comes to ambient temperature, particularly in high humidity areas.
• Cold: Your battery life will be measured in minutes, so you might have to take along an outboard battery for longer shooting sprees. If it gets cold enough, your digital camera won't even function. If you have film, it will become brittle so wind slowly and compensate for exposure.
• Snow: Same as rain. As long as your camera is dry there is nothing to worry about. If you drop it in the snow, wipe it off with a dry towel
• Fog: Nothing really needs to be done. You'll experience the same issue as taking an air conditioned camera out in hot and humid air: condensation on the lens. Fog can produce some fantastic pictures. Wipe down the camera when you get inside, and clean the lens.
• Underwater: Get a water tight case to put your camera in. They're expensive, but open up the world of underwater photography. NOTE: test the case with paper towels on the inside first. You don't want to find out you didn't put the thing together properly with your expensive camera inside.
• Sand storm: Stay inside or put a "throwaway" UV filter on the lens. Nothing like pitted lenses due to the natural sandblasting going on.

The good news is that the professional line of cameras and lenses tend to be sealed against the weather. They can withstand dust, rain, and minor contact with water (not underwater photography though).

Use common sense. All electronics have operating conditions they are designed to work within. If you exceed those conditions (extreme hot or cold) then the sensor won't respond or will be filled with lots of noise. The good news is that most cameras have a wider range of use than you do. All mechanical and film cameras tend to be able to survive even more extreme environments (hot and cold here) than the digital counterparts, but not without their own trials. Too hot and the film will melt. Too cold and it will become brittle and break in your camera. Too dry and you have tiboluminescent streaks. Too many XRays and you have weird sine waves across your film.