These statistics are critical for your survival as a webmaster. 
You MUST know what's going on with your site. 
Is it being visited and who is visiting it? What pages are people visiting? 
These are essential statistics that you must watch carefully and often. 

Why? 
To improve your site and it's ability to fulfill it's purpose. You've put a lot of work into creating a site and you want it to accomplish some goal. In order to know if you are achieving the goal, you must look at what's going on. 

I guess the first question a webmaster asks is "is anyone visiting my site at all?" A hit counter fulfills this need nicely. You can create a simple one with CGI, you can use a built-in feature if you use Frontpage 2000, or you can use any number of free or almost free hit counters available all over the web. 

For the more complex questions I would recommend a good statistics package. If you are running your own server you have it made - lots of tools are available. Otherwise, you would be best served to use one of the free services available. Visit Allfree.gr  and find Free and Low cost search services.

If you are being hosted on one of the many commercial or free sites, it's certain that they have a statistics package of one sort or another available.

But perhaps you're wondering why you need this data? What's it really for? Well, let's say you have written a site to sell stamps. You have four pages to the site. You look at the hit counter and see 400 people visited it yesterday, but only 3 of them bothered to visit your page to see what they could purchase. In addition, you also see that there were no visitors from yahoo.com and only a few from other search engines.

Now you have some things that you can do. You can come up with a better design to get your users to the page where they purchase stamps. You can see if your site is listed with yahoo.com and if not, fix it. And you can check the rankings with other search engines and fix what's going on there.

Another statistic might be monitor size. Let's say you designed your site for 1024X768 resolution. You look at your statistics and you find that 80% of the visitors have 800X600 screens. Additionally, you see that there were few hits on the inner pages on your site. In this case, you might conclude your visitors are being turned off because your site does not fit on their screen. A redesign might be appropriate.