Something is definitely wrong if odd odors are emanating from your PC's chassis. Possible causes of unpleasant smells include blown capacitors on your motherboard (time to start shopping) and a failing power-supply fan (time to start shopping). But the problem might be tied to secondary symptoms: Did your monitor's picture suddenly zip out at the same time that your nose put you on notice? Did your computer lock up? Did it spontaneously shut off?
Your goal is to identify the source of the smell with a particular part. Burning smells can indicate failure in a cooling system (connected to the power supply, video card, or CPU), but they can also develop when you attach a cable backward (often accompanied by a burst of flame), accidentally short your motherboard, or improperly adhere a heatsink to a particular part.
Also, be sure to give the insides of your computer a good cleaning--a gentle dusting might resolve the olfactory outrage.