In the past, I have tried several different ways to skip the first link that Google takes into account for a given URL (nofollowed links, links with 301 redirections, etc). However, all these attempts had little success (301 works but it’s very suspect). Recently, I ran a test to see how Google handled the anchor links (links to different sections within the same page, eg: text)
Or in graphic form: 
Results for Test 1
If you search for the first linked text we can see that we don’t get the results of the destination page (Page B) . This link is not an ‘anchor link’, this link is a link to a ‘simple URL’ (that´s how I named it) but it is ignored.
SERP for first link: simple link (no # mark) 
Instead, Google takes the next two anchor links (this and this) and shows the page they point to in the results. Although the apparent ignoring of the first link is odd, the way the link is displayed is even weirder. As you can see the URL that shows in the SERPs (See red box in image above) does not take to the anchor link, but to the simple link.
SERP for second link: anchor link (#)
SERP for third link: anchor link (#) 
Results for Test 2
SERP for first link: simple link
SERP for second link: anchor link (#)
I ran two more tests to see if the test could be reproduced. Both of the other tests had the same results!
Conclusion
It is interesting to see the impact that link order has on rankings. Keep this in mind going forward and I hope you find this as interesting as I did.
Note from Jen: Errioxa had an updated version in the queue that I missed that explains this all a bit better. I have updated this post with the new version. 3/16/10
