How much radiation do computers (PCs, laptops, etc.) emit? What precautions can users take to prevent/reduce the effects of this radiation?
To follow-on to Ignacio's answer, everything emits various amounts of some kind of radiation.
For our purposes, there's two kinds of radiation that are relevant: bad radiation (ionizing radiation, will hurt you eventually) and not-bad radiation (everything else). I use the term "not-bad" instead of "good" in that it isn't beneficial but neither is it harmful. It's just there.
Your computer and peripherals emit very little or no bad (ionizing) radiation. If they emit any, it's far less than you would get walking around outside for twenty minutes.
That all depends on what you define as "Radiation".
You get some small amounts of Electromagnetic Radiation from all electronic devices. You don't get anything nasty like you used to out of the back of old unshielded CRT monitors (modern ones are shielded and don't emit very much at all).
CDRom drives do have a laser in them which emits laser radiation - only harmful if it is shone directly into the eye.
Heat is also a form of radiation
Other than that, no, nothing. You certainly don't get anything like nuclear radiation or anything of that ilk.
If you are using a CRT monitor (rare these days), it will emit a small amount of X-ray radiation, as does a similar TV. Other than that, I am not aware of any computer components that emit radiation of a type to be concerned with.
With early computer monitors there was some concern, and some operators would wear an lead apron. Monitors were improved to reduce the level of radiation they produced, and the need for precautions was believed to have been eliminated.
You probably want "ionizing radiation", as in a pedantic reading all the light, sound, and heat the thing puts our are "radiation".
To answer the question: with the CRT mostly a thing of the past the biggest sources are probably naturally occurring radioisotopes in the germanium (Ge-68) in the chips and the heavy metals on/in the boards (lots of Uranium daughters). In both cases the quantities are negligible.
-1 for asking a question that you should have researched instead of asked. I Googled "do computers emit radiation" and got some interesting results. Once you ignore the homeopathy and ehow sites, you get some actual sources. Here's some of the more interesting quotes.
From the EPA: source
"Scientists work from the premise that no amount of radiation is safe. Even though most TV sets and computer screens have not been found to give off any measurable level of radiation"
From the American Cancer Society: source
"Electric currents create extremely low-frequency (ELF) electromagnetic fields, which are at the low-energy end of the electromagnetic spectrum."
"Most studies in adults have not found links between electromagnetic fields and cancer."
"Non-ionizing radiation is low-frequency radiation that does not have enough energy to directly damage DNA."
My Understanding of the issue
As someone who trusts science and scientists I believe that the "the absence of evidence is not the same thing as the evidence of absence". We know that the radiation released by computer electronics is non-ionizing so it does not cause direct damage to your body. This has been proven through credible testing and many studies.
What everyone is concerned about is the long term affect of computer based radiation. That can not be easily tested because we are exposed to non-ionizing radiation constantly. On the good side, I do not know of any credible studies that demonstrate that this type of radiation is harmful.
So what does this mean to you? This is not something to worry about. Your more likely to develop a repetitive stress injury from constant computer use. If you are worries about it, limit your exposure. Move the computer and monitor as far away from your body as possible. Turn the computer off when you don't need it. Take frequent breaks and walk away from your computer. This has the added benefit of preventing you from sitting all day.
Hope this helps.