A number of people are trying... there are a lot of other search engines out there, most of them highly specialized.
The Search Engine List
Cuil (Pron: "cool") is the newest trying to take on Google. Supposedly searches more pages and indexes more documents than Google. Ex-Google people have done this startup.
I’ve followed Cuil for some while now, but the pace at which Google is innovating, it is going to be a gargantuan task for them. Google simply is much easier to use than most other search engines.
I find the “search within a website” function on the Google toolbar, especially useful.