Hot Pixels - Olympus
Image noise may be caused by a number of different reasons, but what I will be discussing here is a specific type of noise commonly known as – "Hot Pixels". Hot pixels are more prevalent in long exposure (more than a couple of seconds) low light photography. The problem worsening as the sensitivity or ISO increases.
Hot pixels exhibit themselves as consistently abnormally illuminated or bright pixels.
Depending on the number and intensity of the affected pixels this may not present too much of a problem. In some cases you won’t even see the effects on the printed image. My suspicions are that you would prefer to eliminate these troublesome pixels. You could use the clone tool on your favorite image editing software to address the problem. This would be alright if you only have a few images to process and they are not too badly affected. But, if you are processing a large number images I doubt that you want to spend all afternoon mastering the clone tool, the novelty will wear off very quickly.
There are lots of post processing techniques and tools available to deal with the issue. Some work very well giving excellent results.
Personally, I would prefer to spend more time taking photos and less time in post processing. Fortunately, if you have an Olympus camera, such as the E-300 you are in luck.
Olympus employ a relatively simple, but effective on camera technique to address the issue. Using the "Noise Reduction" setting in the Olympus E-300 the camera automatically takes a 2nd shot with the same settings except the shutter is closed. The second image is then subtracted from the original image resulting in a significantly improved image from what you would have had without using the noise reduction.
There is however a price to pay for these nice clean images. As you are taking two shots each time plus some additional time for the camera to process the image the time between shots is increased. There is also a reduction in the number of images you can fit on your compact flash card. Without noise reduction I can get around 72 RAW images on a 1Meg card, with noise reduction turned on this is reduced to 58 – a small price to pay for the convenience.
Olympus E-300 sample images. The samples taken here all have the lens cap and eyepiece cap on to stop any spurious light from entering camera. Each image is a 150x150 pixel crop taken from the top left corner of the full size image, they have been converted to JPEG and magnified twice.

Sample taken at 100 ASA, 30 Seconds Exposure, F16.
As can be seen there are a small number of Hot Pixels

Sample taken at 400 ASA, 30 Seconds Exposure, F16.
As the ASA rating (or amplification) increases so does the number and intensity of the Hot Pixels.

Sample taken at 400 ASA, 30 Seconds Exposure, F16, with Noise Reduction enabled.
With Noise Reduction enabled there are no obvious signs of the hot pixels!
Important to note - If using noise reduction it does not become effective until the exposure time is 4 seconds or more. So, it is likely that as your exposure approaches 4 seconds you will get some minor issues with hot pixels.
Some image editing/viewing software can't properly display the RAW images which have been taken with the noise reduction setting enabled, neither Picasa2 or Rawshooter Essentials can display these images. Rawshooter Premium does however show them correctly.