The most common myth in the Search Engine Optimization industry is that by linking to popular sites on your topic you will be ranked higher. Nothing could be further from the truth. This myth has been propagated for years by people who do not do any research and who do not understand search engines from a technical level. While this myth has been debunked many times, it continues to thrive due to some very determined individuals who, for whatever reason, have still not managed to provide any empirical evidence backing up their claim.
Before I get into the meat and potatoes of this issue I would like to start with a little vocabulary lesson. First and foremost, what is an outgoing link? An outgoing link, also called an external link or external outgoing link, is a link from a page you own to a page you do not own. A link from a page you own to another page you own is usually referred to as an internal link, or an internal outgoing link. You should also be familiar with the terms "hub" and "authority." An authority page is a page with information about a topic, a hub page is a page that has little information of it's own but rather links to authority pages.
It's hard to trace this myth to one single source. The owner of a large poorly designed webmaster forum said some years ago that outgoing links will be important for the future. To my knowledge he's never supported that claim with any kind of logical reasoning or empirical evidence, nor has he revealed just how his psychic powers work. Also a few Google employees, mostly those from the Public Relations department (not the engineers or the guys in charge), have said that Google checks or "looks at" outgoing links. They have also said that sites without outgoing links are "obvious."
It was that last example that probably really started this myth running. People took the statement, that really wasn't anything more than "Its obvious which sites do not link out" to mean "Sites that do not link out are penalized." This is despite the fact that so many successful sites with #1 rankings do not link out. It was a short leap from lack of outgoing links penalizing you to outgoing links helping you. This example really illustrates how rumors get started. Someone says something, is misunderstood, and then the concept morphs with each retelling.
When it was said that Google "looks at" outgoing links it was seen as vindication of this out of control rumor. In truth "looks at" is vague at best. Google has always looked at outgoing links as a way of passing PageRank. If Page A has an outgoing link pointing to Page B then Page A sends a little PageRank to Page B. Maybe that is what they meant? Or maybe they meant that Google looks at outgoing links as part of a spam filter, perhaps flagging sites with too many outgoing links as possible link farms for human review.
These possibly explanations did not dissuade those who believe in the myth and, despite lack of all empirical evidence, they continued to carry the banner of outgoing links.
Of course, some people thought they had evidence. They would in the process of SEOing their site add a few outgoing links and when they went up in rankings they attributed their rise to the outgoing links instead of hundreds of other possible factors. This act of attributing causation to a single variable when there are many variables is why it is so necessary to conduct experiments where every variable save the one being tested is controlled. Such controlled experiments are the cornerstone of scientific research and something that no proponent of the outgoing links myth has managed to do.
To give you an example, someone once studied a group of school children and found that the ones with newer appliances at home tended to do better in school, would it be safe to assume then that appliances make kids smart? Of course not, that's silly. In reality educated parents tend to have smarter children and educated parents also tend to earn more money, so that they can afford newer appliances. That the smart kids come from homes with new appliances is simply a coincidence, and coincidence, along with conjecture, is the cornerstone of the arguments for outgoing links helping.
The final reason why people believe outgoing links help is somewhat of a karmic one. They believe that its good to link out and that because it is good that it should help you in search engines. They also believe that its unfair that some webmasters do not link out and "hoard" their PageRank, and they believe that Google and other search engines are some kind of Internet referees to make the webmaster community as fair as possible.