I created a site called Search Engine Labs to run search engine experiments on. It was necessary to do this as running experiments on an existing site does not allow you to control all the variables. With this site I can control all variables. Another key requirement is multiple trials and a control group. I did not limit myself to a single test group, but rather three. Through pure randomness a single test group might have shown positive, by using three I limit this possibility. As such all three must have the same results to prove the theory right.
The experiment works by making 3 pages with identical text. On one page there are no links. On another page there is a keyword rich link, on the third page there is a generic link. This was done to test both if the link helped and if the link text was weighted higher.
To run the test you need to search for the target keywords while limiting the results to the site's domain by doing an advanced search. You will find that no single page type; link, no link, or keyword rich link, is always ranked at the top for any of the three test groups. This means that there is no correlation between outgoing links and your site's rankings. If outgoing links did help then the page with no link would always rank last. If outgoing link text was weighted higher then the keyword rich link would always be first. Neither of these are true for Google at this time.
Before I end this article I want to make one very important distinction. Linking to a popular site on your topic does not help you, however, if linking to that site means that you will get a link back, basically a link exchange, then that can help you both with direct traffic and with search engines.
Also, outgoing links do limit the amount of PageRank or "weight" you can send through your internal links. So you may want to somewhat limit the number you have on any one page, but a handful is not going to hurt you any noticeable amount. For more on that please see these articles:
I have little faith that this myth is going to die anytime soon, and it is always possible that search engines may use outgoing links in the future, anything is possible after all. So the search engine labs site will always be up and you will always be able to go back and check to see if anything has changed.
I'm not the type of person who deals in future predictions, I care only for the present. I am not here to say that search engines will never use outgoing links to rank your site. I am here to say that they aren't doing it right now. So, if you want to add outgoing links to your site, do it because you want to link to the site, not because you think it'll give you some kind of bonus.