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What hosting platform is your site on?
Some packages may be available free from your hosting provider and may be adequate for quick summaries, for example I have had a few sites where "webalizer" was included in the chosen hosting package and for a quick review its fine and quite configurable.
It shows for example the top requested pages, referrals and search keywords / terms along with plenty more information.
However it does not split keywords by referrer, rather lumps keywords used together no matter for example if they came from google or msn searches. So if you used webalizer you may have to access and process the raw logs to get down to that level of important detail.
Urchin is another server side stats package I have used on a site on more expensive hosting Urchin allows drilling into each referrer or search engine detail to a great level, so you can for example check down into the referrals for each version of google (.com .co.uk .de etc etc ) or yahoo or msn etc and see which keywords over whatever time period you like .. I found the js menu system bit of a pain but Urchin allows access to loads of data, a more graphical interface than webalizer and a more sophisticated product all round. I liked having that online for me.
These two are server based stats packages.
There are also packages like webtrends which allow processing of log files on your pc and allow the output of custom reports from the data which can be useful if you need regular management reports or the like. I have not seen customisations that I thought cut to the data that is really important from webtrends to be honest but that may be more the person making the report than the programmes abilities.
Then there is the option to import the raw logs yourself into a relational database sytstem and ask any question you like of them, thats the highest level of customisability and some swear by it ... in truth I sometimes swear at mine :-) because some things are not as easy for me to get it to do as the pro programms above make it appear.
From my view however the flexibility of being able to ask any question I want is invaluable.
Anyhow hope this helps, I am sure there are plenty more out there that I have not used and people may come along with more valuable feedback for you.
Its really "what do you want?" in detail .. and what can provide that.
I love it. It takes a while to set up for a bunch of sites but can be modified to do all I need. It can be run on the command line so I just made a batch file that runs it 8 times every night for all the sites that I check on a regular basis. The stats are great and it is cheap. Webtrends does not offer enough for me to justify spending that much more. They do have some nice features but they are not worth that much. I can send you my batch file if you want. You can run it in your office or on the server. It will get the log files via ftp or just on the local machine. It can publish the reports via ftp or local machine. I have it create 8 different web reports. I just made an index.htm that links to each report. You can also have the reports emailed automatically.