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.
 
Ohio Environmental Protection Agency
Guide to Computer & Electronics Waste Reduction and Recycling
http://epa.ohio.gov/ocapp/p2/recyc/comprc.aspx

Goodwill will accept working televisions and computer monitors.  Goodwill will also accept computer CPU’s working or not for recycling.

 Best Buy recycles televisions for a fee at their stores.
 http://www.bestbuy.com/site/Global-Promotions/Recycling-Electronics/pcmcat149900050025.c?id=pcmcat149900050025

Staples recycles computers at their stores
http://www.staples.com/sbd/cre/marketing/sustainability-center/recycling-services/?icid=SustMain:middlecontent:2:RECYCLE:

Office Depot offers an electronic recycling program.
http://www.officedepot.com/a/promo/pages/0928_recycling/