Here are a few reasons...

• Its fast: The home page as well as searches are very fast.
• Relevant results: The first result is normally what you are looking for. You will hardly need to go to the second page!
• Simple design: There are a very few links and graphics on google home page as well as search page.
• Focus on search: Google is search. It's not a portal. At a time when all the websites were trying to provide everything (for e.g. mail, calendar) google focused on search. It was a risk, but it worked.

There are some reviews those say that google name itself has helped to create the brand. I don't agree. I have seen many people typing the wrong spelling to reach to google. for e.g. goggle.com, goglee.com

Thus the "confusing name" is the weak point of google. Now Yahoo has refrained it's search to take on google. It has introduced a new Yahoo! search on April 8, 2003.
http://search.yahoo.com/
Revolutionary concept:
Users can now save their preferences through their Yahoo! ID to use Yahoo! Search the way they want from any computer. for e.g. if I normally search for english pages and open search results in a new window, I will set it up in the preferences. Now whenever I search (while logged in) I will get the english pages only.
This revolutionary step towards user identification will immensely help yahoo to provide more relevant results. And I think this is going to be the next wave on the net after google.
Yahoo knows too much about me. My birth date, location, credit card number all is there in the yahoo database. Now all they need to do is find out the pattern of search queries by saving all what I am looking for. Try to learn what I mean and don't just throw results based on keywords typed.
Is it difficult? Not at all! Let's see if yahoo is willing to do it.