Yahoo and Google (on Slashdot): rooting for underdogs
What I think that Google has is a great distributed computing platform (GFS, map reduce, etc.) that lets them quickly try out a lot of new ideas quickly and scale them up as needed. However other large companies also have great resources (e.g., the best computer scientist who I have ever worked with now works at Yahoo) and in any case, I expect to see most great new ideas come from much smaller groups.
Although playing for market share seems like a zero sum game, I don't think that it is. We don't even know what new and hot markets will exist in a few years. Creativity space seems infinite, to me.
Even with search, I tend to sometimes use 'the underdogs', mainly because I like to see competition, and trying competing products seems right. I think that the Clusty.com clustering search engine is both very cool and useful. I am a voracious reader, so using Amazon's A9.com search engine is fun because I get web, book, people, etc. search results.
Google provides a good service, and I am happy to see them rewarded with the largest market share - as long as perhaps a third of the market is left for other companies. If Google ever achieved Microsoft-like search market dominance, I would probably stop using them, even if they were technically the best. Anyway you look at it: free unfettered competition is good.