I have done cleaning myself, but it is a delicate operation and not for the timid. Since I have a background in electronics and optics, it isn't something I am afraid to do. But you have to be careful doing it. Most of the time, a rocket blower will remove the dust. Set the mirror lock in the camera menu, tilt the camera so that the lens opening is facing the ground, and use a blower to blow out the dust.
Now when you have been in very dusty conditions, or doing air-to-air work, the dust really gets in there, and can be stubborn. This is where it gets a bit riskier. I take a wet lens cleaning cloth, the kind that are sealed in packets and are dust free, wrap in it a Q-tip (cotton swab) and gently clean the sensor. You have to make sure that the swab stays wrapped because they are usually full of particles that can actually make it worse. I only wrap the lens cleaner in the q-tip so that I have a soft surface under the cleaner.
Once you are done, make sure that it is completely clean and dry. If you leave some of the wet solution on the sensor, it can produce spots too. Then take some test shots of the sky, or a white piece of paper and make sure that you don't have any spots still there or that you didn't leave a dust bunny in there (it has happened to me).
You can also use canned air to clean, but be careful not to tilt the can too much, which can cause the propellent to come out wet, which can spot the sensor glass.
On the Nikons, the actual sensor is behind a piece of glass which also acts as a filter. So unless you are particularly ham-fisted with the operation, it is a fairly safe procedure. There is a way you can actually disassemble the camera for cleaning, but I would recommend against that as it requires a soldering gun, lots of screwdriver turns and some steady hands. I leave that kind of cleaning to the pros.
Additionally, there is a company out there that can replace that filter glass over the sensor for infra-red photography, or full spectrum. Both are kind of cool, but very specialized. I am thinking about converting the D50 to an IR or full spectrum camera after I get a D300, but am syill not sure if I will.