First, let me say that PageRank and ranking in the SERP are two entirely different things. Many folks get those two things confused. The way your question was asked left enough ambiguity to generate mixed responses, relating to these two very different items. Let me address each item separately and in turn.
PageRank, which is named after Google co-founder Larry Page, is a relative score based on the number of direct and indirect incoming links to a URL, represented using a logarithmic scale of 0 to 10. No amount of outbound links has any effect whatsoever on your PageRank score.
This PageRank score is used to weight the value of relevant outbound links from that page to its destination page. This relative weighting value is divided equally among all the different outbound URLs. It’s important to note that outbound links do not drain any PR from the page where they are placed. Instead, those outbound links dilute the weighting value that influences the linked-to page (not linked from the page). The page where the link is placed is not diminished but the weight and influence those links have on the landing page is diluted.
So, when you link out to lots of other pages there is no negative effect on your page, you are simply dividing the benefit that is passed to those destination pages. The only thing that affects your page’s PR is the inbound links to your page.
Now on to how links affect your SERP ranking. Your pages are ranked in SERPs based primarily upon your page’s relevancy score for the keyword term used for that search. Both inbound and outbound links to and from your page will influence your page’s relevancy score. Your page”s PR score has virtually no direct influence on where your page will rank in the SERP.
Backlinks are important for ranking, but not for how they influence your PR score, but instead for how they influence your page’s relevancy score. Outbound links can be just as influential as inbound links on your relevancy score.
Some folks pursue the practice of hoarding PageRank. Accumulating PR does not help your page rank for a particular keyword, but it does increase the influence your page’s outbound links will have on other pages. By linking to fewer pages you can concentrate the power of those few outbound links you do place.
There are many other considerations when creating your web of links, this explanation is meant to give you an idea of the basic concepts.
