I was going to give you a breakdown of the free site stats out there, but then Google announced that they are giving away their statistic analytics software for free! Google bought Urchin On Demand, a terrific site statistic program that captures which pages were viewed, which pdfs were downloaded, which files were hit, referrals, etc. Normally it's about $200 a month to get, which is crazy. But now it's free, and even more free when you use their AdSense program (so it's really a giant push to get more advertisers on AdSense, which is fine).
Here's what Google says about it:
Google's strategy is amazing! They are crushing competitors by offering major things for free. This may have a trickle down effect, as I'm already free now to move hosting companies for my website. I am paying $24.99 to a hosting company to host my site only because they offer Urchin. But now that I can get it for free, I'm free as a bird to pay $10 or less to a company that does not provide Urchin as part of their hosting package!
The other free site stat program you could consider is StatCounter.com. At one glance, they give you the referal, location (city, state, country) and entered and exited page. I use both programs in order to get up to the minite at-a-glances (thanks StatCounter) and comprehensive stats (thanks Urchin).