Before Google hit the scene big time in the early 2000s all linking partnerships between sites was for traffic reasons. You might find a site that offered a complementary but non-competitive service and do a link swap (reciprocal link) between the two sites.
Since the rise in dominance and importance of Google, it is necessary to employ linking strategies that avoid direct reciprocal links if maximum value it to be achieved. That is not to say that a good traffic bearing or similar themed reciprocal link is to be avoided.
If you can arrange different types of links (like those listed below) your site, and your partners will appear higher in the search engine rankings as a result.
One Way Link Partnership
This is the simplest type of link. You have got a one way link to your site from another.
You are not giving a link back in return. This is the best type of link. For a link like this from another site look at submit article - you control the content of the linking page.
Reciprocal Link Partnership
This is the simplest type of link partnership. You have got a one way link to your site from another, and you are giving a link back to the same site.
This type of linking is useful but not a good as other forms of linking.
If your sites are of a similar theme; complimentary and non-competitive, or you expect worthwhile traffic this link arrangement may be for you.
Open Jaw One Site Link Partnership
This is an advanced link partnership. You are linking your partners site and he is linking another one of your sites from his.
This type of linking is can be as good as two one way links, but matching the strength and quality of the links in important.
Split Pair Link Partnership
This is an advanced link partnership. You link a partner site, and in return he links a different site of yours.
This type of linking is as good as two one way links, but matching the strength and quality of the links in important.