While "Yahoo" is the top search query on Google, Yahoo seems to be in a similar shoes vis-a-vis the term "Google." Yahoo, however, deals with it a little differently than does Google. As reported at Slashdot:

"Google Trends indicates that over the course of the past year the search term "Yahoo" became more popular than "sex", making it the #1 query on Google. Yahoo apparently faces a similar dilemma with roles reversed: When you search for "Google" on Yahoo, Yahoo thoughtfully displays a second search box as if to tell you, "Hey cutie, you have a search engine right in front of you!" A puzzling phenomenon? An strange aberration?"

Unfortunately, at the time of this writing, the more popular than sex link embedded in the blockquote is not functioning. It seems that Daily Domainer's server is down for some reason.

My guess, however, is that the vast majority of users who are searching these Search Engine's respective competitors is that they are looking for news and auxiliary services (such as Google Reader) rather than the search engines themselves. After all, I think that the average user has become savvy enought to figure out that adding a .com to the end of a name as large as Google or Yahoo is sufficient enough to get you the desired result if the search engine is indeed what you're looking for.