[artdutra04]

If you use a welding helmet/glasses* with a shade protection of at least 13 (14 or higher recommended), you can observe the sun [during an eclipse] with your own eyes. If you use this same level of shade protection on a camera, this should protect the camera's CCD/CMOS sensor from the infrared, visible, UV, and cosmic radiation for somewhat extended periods of time.

Also, when trying to photograph the sun, never use telephoto lens (or anything larger than 200mm zoom), as this will begin to expose enough of the sensor to the sun to start doing permanent damage very quickly.

Otherwise, with most point-and-shoot digital cameras, you can take occasional pictures with the sun partially or fully (such as with sunsets/sunrises) in the frame without any problems. On my older digital camera (which was about 23,000 pictures old before I retired it), I estimate that I took several hundred photos with the sun in the picture without any problems.

* Don't use oxyacetylene glasses, as they typically offer only a shade protection of 6, which is no where near enough protection.