I've heard there are some companies that offer a service to extort websites that include information about you (such as Reputation Defender mentioned in this article: http://www.washingtonpost.com/wp-dyn/content/article/2007/03/06/AR2007030602705.html). So, you pay a company that then harasses websites that have stuff about you on their site. I assume this works for companies, personal blogs, discussion boards, etc. Other places like government agencies who have information online may be more difficult to work with. I can't imagine you can have your name entirely stricken from the Google/Yahoo index. Plus as you mentioned there would be problems with "identity confusion" (which Jane Doe to eliminate).
You can request that pages you own be removed from the indexes (here's info from Google: http://www.google.com/support/webmasters/bin/topic.py?topic=8459). So if you used to have a webpage/blog/etc, you could try to have it removed from the indexes. Really someone who wants to be "unlisted" should make sure their telephone/address listings are unlisted (and contact any companies that list you), never sign up for anything, use an alias with an unidentifiable email that no one knows is you (i.e. don't share w/ your friends), never create profiles or in any way add information online. Keep doing searches and approach those businesses or agencies that list you individually to ask to be removed. You can make DMCA (Digital Millenium Copyright Act) requests to have your own copyrighted content taken down.
