How can I purge unsavory results from searching my name in a Google search?

See hints from http://www.google.com/support/forum/p/Web+Search/thread?tid=70f6a8609a4486c8&hl=en there is a chance you can minimize impact. Official Google point of view on the topic is at http://www.google.com/support/webmasters/bin/answer.py?answer=164133

Just in case you're still looking for a bit more info, one of our Top Contributor's in the Google Web Search forum posted this great summary of how to remove content from Google: http://www.google.com/support/forum/p/Web+Search/thread?tid=2856d612feeb1e71&hl=en

Replace it with better search material. Create a website with more searchable content, blog, social media is HUGE. If you do not have the time to do these things yourself then I would suggest hiring a reputation management company (a niche SEO company) that specifically deals with this exact issue. Hope this helps!

Other than  asking for the unsavory results to be taken down from the respective webmasters (may be unlikely), the only way to exercise some real reputation managment is to replace those results in the SERPs with your won pages, as has been suggested. Assuming those pages with unsavory results are not NewYorkTimes or Wikipedia, etc. then it should take you around a month, maybe quicker.

If it is web presence you can always use an alias or initials until you get your information corrected. Sometimes it may take a minute for you to remove or change results. In the meantime, do your best to use a name that does not result in the bad information coming up. Perhaps use even a middle name or nickname. Its the web ... you not required to disclose everything about you. Its your right to change your name or use an alias. Take advantage of that. The person that put the bad information is counting on people using and knowing your known name and information.