If you are site owner (or can look like one), you can use Google’s tools to remove items from Google rather easily. Adding things into Google is substantially harder.
We recently changed the department’s site from http://www.eng.uab.edu/ece to http://www.uab.edu/engineering/home/departments-research/ece. Not my choice and there are some real issues with the increased depth of the URL but we still need to convince the search engines to list us for search terms like “UAB ECE” and similar terms. Fundamentally, it takes time because there are not many links to the new site just after a change.
Updated 24 May 2013: The “new” URL changed again for the department web site.