A reciprocal link exists if website A links to website B and website B links to website A. There is more misinformation and obfuscation on reciprocal links than almost any other subject because mutually agreed link exchanges are falsely believed to be 100% effective in achieving high search engine rankings.
Whole businesses have been built around link exchanges and millions of site owners have bought into the myth. Lured by extravagant promises they have purchased automated link exchange software or indulged in organized link exchange schemes only to discover that their site never achieves their objectives and sometimes even gets banned by the search engines.
(Before you read on make sure you have read Outbound Links and Inbound Links.)
Remember the example of good outbound links?
Here is one of the sites on the page linking back.
Remember the example of poor outbound links?
It was from a site selling ethnic jewellery and here is a section of a ‘links page’ from one of the sites linking back.
This site sells ringtones and has many link pages that are similar, all stuffed full of reciprocal links.
Looking at these (admittedly extreme) examples we can see that reciprocating a link will not automatically make a good link bad or indeed make a bad link good, what is important are the individual links themselves.
Reciprocal links can be good or bad but thinking of reciprocal links as entities with their own different set of properties (like good or bad) is counter productive, so just think quality links.
May 19, 2006 Additional information available here, Reciprocal Links (Update).