To answer that question we first have to find out what Search actually is. What solution does Search offer and when do you need Search?
The question: When exactly do you need search?
The answer: When you don’t know where to find something
So what if you did actually know where to find everything?
If you are looking for People, yes, you might start at Google. But there is a pretty good chance you will Find those people on Facebook, LinkedIn or any other Social Network. When it comes to searching for friends Google is NOT the preferred search solution. Social Networks are.
If you are looking for a book you will probably visit Amazon before Google.
Second hand stuff? You Search for and find it at eBay.
A cheap flight? You would use Expedia or another travel website.
Words or definitions? Answers.com and WikiPedia.org, of course.
Music and movies? iTunes, BitTorrent and Amazon.