I also have dust on my sensor but have never cleaned it (for the 3 years that I've owned it). Cleaning it depends on the camera though. I have a DSLR so its as simple as taking off the lens, having the camera move the shutter open and blowing out (with air, not compressed air, there's actually a product that looks like a fat turkey baster thats sole purpose is to blow dust off the sensor glass) the dust. If its not coming off there are wet methods and other products to clean it. There's also sending it to Canon (or Nikon, Pentax etc) so they can clean it but that cost money.
As far as Point and Shoots and larger cameras without removable lenses, I'm not sure. Since the sensor and sensor glass aren't easily accessible, I'm thinking it needs to be sent in to the manufacture for cleaning.
Just a note, Sensor dust is usually seen due to stopping down a lens beyond a certain point where sensor dust become illuminated (I believe is the case). In regards to my DSLR, sensor dust really isn't apparent until I stop my lens down to f/11 which is an aperture I rarely shoot at (even with landscapes. Since I own a APS-C camera, I get enough Depth of Field at f/8). The more you close down the aperture (f/16, f22 and beyond) the more apparent the sensor dust becomes.