Unlike Yahoo or MSN Windows Live, Google is not offering feeds to their search results, besides Google Custom Search, and new API keys are no longer available. If you want to monitor a search query, you can use Google Alerts or Google Alert [this is not part of Google, and is completely a different & independent servie]. But feeds are easier to manage and consume.
Until Google decides it's a good idea to provide search feeds or a new API, some "evil" people came up with Evil API, a replacement for Google SOAP API, and Evil RSS, a way to get feeds for search results. Both solutions are open source and use screen scraping (what else?) to get the results from Google. That means the solution is not quite OK if you look at Google TOS:
"You may not send automated queries of any sort to Google's system without express permission in advance from Google."
If you don't send too many queries and/or host the code on your server, I'm sure Google doesn't mind. Many Google Gadgets use screen scraping to get search results (and information from sites that don't provide feeds), and Google makes it easy to do that.