A Google Groups thread has a long discussion on how Google defines what a link farm is or is not. I have decided to isolate a Googler's comment, because who can best define what Google feels a link farm is, better then a Google employee?
JohnMu, a Google Webmaster Trends Analyst, posted twice in the thread. The second time he offered additional advice on how he would define a link farm. He said:
A good rule of thumb is to ask yourself "would I be doing this (linking there) if search engines didn't exist?"
Another way of looking at it is to think about where and how you will be linking: Do you feel fine with linking to that site with a highlighted link in your main content or would you rather have the link in 5pt gray on white in the footer? Do you want your visitors to see and use it or is it just for the search engines?
John also links to the Google link schemes page which has the official line on bad linking. Now, of course there is gray area and that is where John's post above comes into play. Even with that, people still may be confused. Well, if it feels wrong - then it might be.
John admits, even him being a Googler, it is still "hard for [him] to provide a definition of what Google sees as that."
If you need more clarification or have specific questions, you can join the Google Groups thread and hopefully be aided in the right direction.
Forum discussion at Google Groups.