Link farms are sites that are set up to contain massive numbers of links to other sites, in hopes of raising the search rankings of the sites they link to. This doesn't work - in fact link farms can now have the result of lowering the search rankings of the sites they link to, because search engines penalize sites that try to use those kinds of tricks.
Personalized link exchanges like those set up with LinkMachine are very different - they are completely search engine friendly. A link exchange is a legitimate agreement between two webmasters to exchange quality, relevant links with one another. These are the kinds of links that make the web as useful as it is, and search engines take these links to your site as confirmations of its quality.