AWStats and Webalizer are both good and free (I think both free speech as well as free beer). I generally prefer the look of AWStats - it has a nice modern look whereas Webalizer looks like something created in about 1992.
They both give roughly the same information which includes:
- Most frequently accessed pages
- Which hosts (IPs and Domain Names) visitors come from
- Proportion of users using different browsers
- Proportion of downloads of different file types
All of this information is usually viewable on a hour by hour, day by day, month by month and year by year basis. Normally the raw data is available but also with bar charts and pie charts. Both AWStats and Webalizer will (I think) try and work out where your visitors come from by using services such as GeoIP, although I never bothered to set this up. Some also try to work out what order people have visited pages in and things like that - but that is very difficult to do so the results are guesses at the best.
I generally find them both useful - even if just to get an overview of what is going on with my server and who is accessing it. They are both relatively easy to install - although I seem to remember Webalizer being a little easier than AWStats, and they both have varied configuration options to let you decide exactly what you want to get out of them.
For more information see their sites at awstats.sourceforge.net/ and http://www.webalizer.org/.
Hope that helps.
Robin