I use Webalizer and like it as well, although it took a few changes to the default configuration to make it behave. In particular, the defaults have it counting internal pages as referrers, which is pretty useless. A one-line change in the config fixes that. (I can look it up if anyone needs it.)
Dominique, Webalizer relies on the same weblogs as all the other webstats software you mention. It can’t give you referrer information on type-in traffic, unless the visitor is using a browser that transmits the current webpage as a referrer even if the user typed in a new address rather than clicking a link. I don’t know which browsers do that, but I know some have in the past.
If that information is present in your server logs, any of the noted stats software can access it.
I would think most current browsers would definitely not do that, as it’s potentially a security issue. Imagine if you’re visiting some site with a password and username in the URL, then type in another website. The webmaster on the second site could grab your username and password for the first site from his web logs.