Supporting SquirrelNet's ranking of Google as #1 in our Top 20 Search Engines list, WebmasterBrain.com has ranked Google #1 in terms of search engine relevancy by head-to-head-to-head blind testing against Yahoo and MSN. Google is listed as having the most relevant results 39% of the time vs. 34% for Yahoo and 29% for MSN Search.
Here is the Search Engine Experiment. Just type in your search phrase, hit Search and you'll see 3 results from each of Google, Yahoo and MSN. After visiting some of the sites, you can vote on which of the search engines provides the most relevant results. The search engines are listed unbranded, so you don't know what you're picking. This lends credibility to the test.
Of course, the user experience at the various sites can also improve the searching experience. While Google has the most relevant results, it also has the best user experience. Thus, in the real world, this explains why Google is preferred by an ever larger margin.
By the way, SquirrelNet also ranks the Google SafeSearch for Kids as the #1 search engine for kids.