This is a very interesting piece from the Seattle Post-Intelligencer quoting Yahoo!'s CFO Susan Decker on the implied unliklihood that Yahoo! will gain any significant search share from Google in the immediate future.
Recall, however, that overall Yahoo! is number 1 in terms of uniques (a position it has traded with AOL back and forth).
What is amazing is that Google grew search market share (by all accounts) in 2005, a year of incredible competition. This year promises to be at least as competitive and Yahoo! may turn some attention from search per se to other assets (e.g., video, mobile, content creation, podcasting and so on).
The Yahoo! Go strategy playing out will also be an important one to watch. (There have also been rumors that Yahoo! will seek to buy TiVO.)
I would also make the unsolicited recommendation that Yahoo! devote more time and attention to MyYahoo (though the company recently "AJAX-ified" the content modules). This is an application that is very strong (for the mainstream user) and should be leveraged sooner rather than later.
On the advertising side, Yahoo! will likely try to continue to leverage its relationships with national advertisers—display ads were an area of growth for the company—and the success it has had in its initial trials with behavoral targeting. Yahoo! is also slowly developing its contextual product.
Local is also an area of great strength and innovation for Yahoo! And, as mentioned, social media and community will continue to develop at Yahoo!
We sometimes forget that there's a great deal more going on on the Internet than search, even though search has become the driver or starting point for so much commercial and non-commercial activity.