How much radiation do computers emit?

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.

tl;dr: no.

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.