Nope, but they seemed to have a smokin' first mover advantage. They absolutely did. Viral, clean, elegant and great results. Like any great software institution, feature clutter, the continuous ebb and flow of fickle user interest, and people getting fat and happy off of their options gets the better of most of Silicon Valley's break aways over time. And Wall Street oh Wall Street, "do I no longer please you?" It happens to everyone, GOOG. What would financial markets be without new starlets all the time. Irrational exuberance and rational pragmatism - two cousins that hate each other, but absolutely can't live without one another.
Will Google be a big part of the web experience for some time? Sure they will. Will they be the gravitational center? Unlikely.
Take a look at this quick comparison of page views.
While there are hundreds of ways to poke at this, I am going to just keep it simple. Look at what has happened to Baidu and look at the other three. Clearly the concept of where and how you find content is changing. Search is adding context - friends, dating, maps, encyclopedia topics, video and a whole Yelp more. Google can certainly try to keep on top of all these trends, but it is a losing battle. No one company is going to own all or even most of the web search behavior of human beings because search as it turns out is actually just an attribute of other behaviors.
Google is a learning organization, however. They saw this coming years ago. Their strategy of offering advertisers a bundle of possible advertising methods is a winner and the next real battle front in web advertising. Microsoft clearly sees this. Anybody else? Baidu?