This article deals with the basic classifications of links. Links can be broken into many categories and types, and having the basic knowledge of what each category means is important. This article does not go heavily into actual linking strategies, since that is a far broader subject.
Reciprocal linking is a classic and very common type of link. Also known sometimes as two ways linking, it is basically the process of link trading with other webmasters. It's the whole idea of 'You link to me, and I’ll link to you'. Oftentimes you will see websites with a 'links' page someplace on their site, often buried at the bottom someplace. These pages are filled with various links to other sites that hopefully have something sort of in common with the site you’re visiting.
Reciprocal links are falling somewhat out of fashion lately in favor of one way links, which are considered more powerful, and requiring less maintenance. It is widely thought that the search engines recognize the links are reciprocal ones and give the link somewhat less weight than if it was just a one way incoming link. One other issue with reciprocal linking is that once you setup a reciprocal link with another webmaster, you have to return to their site occasionally to check and make sure your link is still actually there. Overall this is still a powerful way to get links however and should not be overlooked.
One Way Links
One way links are links that are incoming to your site, but are different than reciprocal links in that you don't have an outgoing link back out to the site that linked to you. For instance if I throw up a link to the Google homepage, that’s a one way link to Google. They are not putting a link on their homepage back to here, though wouldn't that be nice! This is essentially the most basic type of linking there is, but it can also be the most powerful.
When the search engines go through someone’s site and see a link to your site, they give weight to your site. When they see that you are not linking straight back to the site that linked you, that you don't have some sort of linking agreement going on, they give it more weight as a link. The assumption is that someone of their own free will linked to your content, and did not require you to link back to them to do it. If that is the case, then your content must be of high quality. Since one way links are so powerful, and don't require any ongoing maintenance, most linking strategies out there today revolve around one way links of some form.
Three Way Links
Three way links are a variation on reciprocal links. However instead of the 'You link to my site, I link to yours' idea, the correct term would be 'You link to my site, I link to yours from a different site of mine'. It's basically a reciprocal link, but your incoming link is coming from some 3rd site instead.
It is thought that the search engines don't particularly care much for three way linking. The thought is that you may be trying to fool the search engines into thinking you are getting a one way link from someplace, when its really just a reciprocal link in disguise. One use of three way linking that is common is for when you have 2 very popular sites, and one brand new one. The idea is that 'I link to your brand new, unpopular site from my very popular site, and instead of me linking back to you from my new site that isn't as popular. I will link to you from one of my other, very popular sites so you get a better weight with the search engines'. Three ways linking is fairly common, but I don't do it and I would not recommend it.