Back Links Defined
Back Link – a textual or image link TO another site – usually included for the benefit of your visitors because it contains important information relevant to your product or service. Usually set to open in a new window so visitors don’t “lose” your site when they open the link. Outward links are of minimal value to your search engine rankings – unless you have a lot of them relating to a common “theme” – in which case your site might be perceived as an “Information Hub” for referrals on a specific topic.
For example, it might be appropriate for a medical-related site to provide links to support groups, goverment/health agencies, doctors and pharmacies with whom they work etc.
Affiliate Link
You place a link to a provider in order to make a commission out of selling their product/service to your visitors. There is zero value in terms of search engine rankings. And of course, there is no point linking to them if you are not going to sign up and sell their products! 
BACK LINKS:
Reciprocal Links & Exchanges
Where two sites agree to provide LINKS TO EACH OTHER for mutual exchange of visitors, and to increase the relative importance of both sites by increasing total incoming link count. Reciprocal links have value in terms of improving search engine rankings, although this value has diminished in recent times. It is still a “natural” form of linking and should not be avoided – just apply this test – “Will the link lead to relevant information, of value and interest to my site’s visitors?”
If the answer is yes, then by all means exchange links. Done properly, constrained to sites with a similar theme, this may also lead to your site being perceived as an “Information Hub” for referrals on a specific topic.
1-Way Back Linking
A link to your site, not requiring a link in return. These are the most valuable form of linking in terms of search engine rankings. Usually these are from clients – e.g. a manufacturer such as Sony/Toyota/Kodak will have a gazillion 1-way back links from retailers, users etc, as will government agencies, airlines, academic institutions etc. This can lead to your site appearing to be an “Authority” on a specific topic.
In most normal web site situations, your main source of good 1-way back links will be Web Directories. In these, a listing in the most relevant category can provide a very valuable “reference” or “testimonial” for your site. Because most directories are human-edited, the search engines place greater value on such links and the well established ones are often regarded by the search engines as “trusted sites.” The more important the directory, the greater the value. In the case of Google, they place huge importance on a site’s inclusion in The Open Directory, and also in the Yahoo Directory… It is important to select the most relevant category in which to have your site included – the content of the page in which the link is contained may also be assessed. 
SE’s Changed Link Evaluation
Google bases approx 50% of its assessment of your site relevancy to a specific search on the site’s that link to you, and on the words contained in the links pointing to your site.
Yahoo has recently filed for patents for technology similar to Google’s Page Rank assessment mechanism, and is expected to gradually implement a similar emphasis on incoming link quality.
It is important to specify HOW the link to you should be implemented on other sites – and to that end I always add a “Link To Us” page on any site I work on, which specifies the exact wording to be used on links TO you.
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