For a start, Google has recently released Urchin under the new brand of Google Analytics. That's cheap as free, and incredibly comprehensive, although under high demand so it can be slow and I suspect somewhat unreliable. Nothing else comes close to it for no money though (Urchin retailed for several hundred dollars before Google made it free).
Webaliser or AWstats are two more free packages (both server log analysis if I recall correctly) which are a little more readily understandable.
) gets my vote though, for usability and quality of data. Cost $4 to $9 per month depending on the package you go for, and has everything you could ever want without being overwhelming.
I wouldn't rely on a hosts own stats, I have found them to be inadequate in terms of the options you get and generally pretty slow to use. of course that could just be the hosts I've picked in the past.
Hope that helps,