Computers and other electronics need to be recycled or disposed of properly due to the possible hazardous materials that many of these items have. Many electronics retailers are now implementing recycling / disposal programs for monitors, computers and other electronics for little or no fee.
List of Hazardous Materials
This list from Wikipedia's Electronic Waste article details what dangerous chemicals are found in electronics.
Mercury : fluorescent tubes (numerous applications), tilt switches (pinball games, mechanical doorbells, thermostats). With new technologies arising, the elimination of mercury in many new-model computers is taking place. 
Lead : old solder, CRT monitor glass,lead-acid batteries, some formulations of PVC.  A typical 15-inch cathode ray tube may contain 1.5 pounds of lead, but other CRTs have been estimated as having up to 8 pounds of lead.
Polyvinyl chloride Third most widely produced plastic, contains additional chemicals to change the chemical consistency of the product. Some of these additional chemicals called additives can leach out of vinyl products. Plasticizers that must be added to make PVC flexible have been additives of particular concern