We use multiple tracking mechanisms -- often 3 or 4 different ones for the same site because they are all better at one thing or another. Google Analytics; StatCounter; Sitemeter; and Webalizer or AwStats that my hosting company provides. And like VanGogh says, their results are all a little different.
Google Analytics is good, but in my opinion it is a bit of overkill if all you want is to do is track straightforward traffic numbers, such as the number of visitors, where they came from, and pageviews. Analytics is much better suited for helping you understand how EFFECTIVE your site is once the visitor gets there. Analytics can help you understand which links or buttons are getting clicks and which are not, how many people sign up for your newsletter, how many abandon a shopping cart, and so on. It is quite amazing what it will tell you about your site.
(Now if I just had time to fix everything that isn't working the way I want it, I'd be a millionaire.)