What's the best website visit tracker?

I have had Nedstat as the visit tracker on my website for a long time (the free version). It's OK, but I want more! I would like to be able to analyse and keep track of the search terms used to get to my website, and also do some analysis of where and when hits are made.

So I wonder if people reading my journal (a very select group) have any recommendations on visit tracking software they would care to share with me? I wouldn't mind paying a small sum for it; free is good, but useful software is better.

An example of what Nedstat produces for my home page is here.