This is a problem specific to digital reflex camera's. Not so many people are aware of the issue when they buy the camera. There are dust particles inside the camera, and when switching lenses (one of the main advantages of a reflex camera), you can get even more dust particles on the sensor. This is almost unavoidable on the longer term, even if you are very careful. There are different ways to get rid of the dust: the easy way is for non-sticky dust: blow air on the sensor, but never used canned air (can leave other stuff on the sensor), blow air yourself (giving condensation, and if you are not careful, you'll spit on the sensor filter, ruining everything), use something like a Giotto rocket blower... here is a picture of the cheapest version (there is a bigger one I would recommend)
Use it with the camera pointing down as explained in your user's manual.
If this is not working, you have to use more serious solutions and the one I recommend is to use sensor swabs in combination with the appropriate fluid. The ones I have been using are coming from Eclipse and are working pretty well. This solution is very expensive and should be used only when everything else fails... but anyway it is better than having grey spots in all your pictures.
More information about the swabs can be
found here:
http://www.photosol.com/
Other serious products (for sensor cleaning using a special brush or other types of swabs) can be found on http://www.visibledust.com/
The last thing you can do, is to send your camera to Nikon for a general cleaning, but this can cost some time (depending on the service organization and the country).
There are lots of people using other techniques I will not and cannot recommend (using a piece of tape, risking to destroy the sensor, or using Q-tips, risking a scratch or more dust on the sensor). Some might work but you have to ask yourself if you can afford a damaged sensor (filter) and the consequences of not having a camera for some time....
This is my typical cleaning kit, I always take when traveling:
There is a new cleaning
technique using tape which seems reasonably safe.
More
information to be found about that new technique on the following site:
http://www.dust-aid.com/index.html
Here is a video explaining that specific technique: http://www.dust-aid.com/instruction_video.html
There is also a recent change in the Eclipse products (2007). Personally I still don't know if this is a hoax or not. Photographic Solutions released a new version of their cleaning fluid, called Eclipse 2. Based on the information on their site, that new fluid would be required for a number of sensors including the D70 and D80, while the D200 and D2Xs need the original fluid. The Eclipse 1 and Eclipse 2 fluids seem to be very pure methanol and ethanol respectively, and the filter coating above the sensor could be destroyed or at least damaged if you don't use the right fluid. Knowing the number of sensor cleanings taking place each year, I cannot imagine there is a serious risk if you are using the original fluid on all sensors. Up to you to decide what you do. The information can be found on the site http://www.photosol.com/
Another very interesting tool for sensor cleaning is the Delkin Sensorscope