Most affiliate programs or other types of scripts (such as top sites lists, or anything that ranks sites based on the traffic they send you) rely on tracking code appended to the URL. This makes it unlikely that the link will provide you any link popularity, as the URL is so different than URLs normally used to access your content.
However, with some server side programming that checks the HTTP_REFERER variable you can instead allow people to just link to your site normally and get credit for those links. Its true, this type of tracking would not work for email marketing, it would not work for people who have software that blocks this field, it would not work for RSS feed based promotion, but on the other hand it would work well for anyone who runs a site with user submitted content. If you ran a popular forum and were a member of an affiliate program that did this you could get credit for every link your users make on your forum to this site, without any tracking codes needing to be added to the links.
The biggest benefit though is to the site doing the tracking. Regardless of what type of site you have, having such links devoid of tracking codes will make them look more legitimate and will make sure they provide the full link weight and link context bonus.
For a site with an affiliate program using this is straightforward, you just change your tracking. However it isn't just sites with affiliate programs that can do this. Also sites with traffic ranking top sites lists can do this, but also directories. Right now many directories require reciprocal links to be listed, which makes them look spammy. Rather do not require reciprocal links to be listed in your directory, but provide this sort of a referral system for listing enhancements.
Still, the largest benefit will be to those sites with affiliate programs. A site with a popular affiliate program can have thousands and thousands of incoming links that aren't being counted because of complicated tracking codes & redirects. Doing this would instantly give you a huge number of real incoming links instead. Additionally it may help control publisher abuse, as they'd only get credit for promoting your site on domains you have approved, and they wouldn't be able to use email spam to promote your business.
For more on this topic please see this blog post.
I saved the best for last so that you'll take it with you when you're done reading this article. I also realize that I touched on this at the beginning in my talks about link baiting, but it is so important that I need to touch on it again.
Gaining incoming links can be easy, or it can be hard, it depends entirely on if your site is good or not. If you put no work into producing a quality site and instead merely plan to focus on promotion you will not have much success. You cannot promote a lemon. If your site is not finished, or doesn't have enough content, or otherwise has a quality problem with it hold off on promotion until it is fixed.
Every single method I've mentioned in this article will be easier, or more fruitful, if you have a high quality website with good unique content. You will also gain more links through no effort on your part if you have a good site as people will naturally link to and recommend your site.
I've provided a fairly comprehensive list of things to try when working on building your link popularity, however if there is one thing I want you to take away from this article, it is that the most important thing is building a quality site. Make a site that people will love, and they will love you for it.
For more on building incoming links, or questions about anything in this article, please see our forums.