What Apache/Wordpress logging/analytic software for dedicated server?

My adventure thus far has me thoroughly convinced there's few things more important than "knowing your sucker..err..audience/customers." So far I've relied pretty much 100% on google analytics. With a dedicated server, are there any http/apache/wordpress logging/analytics software that are available that would provide more/better information than google analytics? Maybe lay the base for building my own niche related database of foundation data so I can more effectively market the right material to the right people, or even sell the data. I know the scope of what I'm asking could easily get lost into something like "so you want to be your own google?" and the short answer is yes I do lol.

But to be realistic let me rephrase and summarize: I am the king shit lord and emperor of a tiny microcosm of the digital world respective to anyone visiting my ded server (yes I'm being realistic haha) - with plenty of resources/scripting knowledge to offload and analyze large amounts of log data if needed (i.e. not averse to acquiring a beefy VPS or secondary ded to focus on this aspect if required). What sort of logging/analytics software if any are out there that I should look into that would help me learn more about my traffic than google analytics?

Really appreciate any help/thoughts/feedback here.

For something similar to G.A. use Piwik.

For log analysis use awstats or webalizer.

When you use google analytics, you're basically handing google all your visitor data. I regret to see so many sites giving google all they need to destroy organic SEO and try to force all commercial sites to buy adwords.

There's a tool called Lucky Orange which records your visitors movements, clicks, and typing on your domains. This can be very useful for understanding exactly how customers interact with your website and over time can be used for conversion optimization.

thank you very much..that is exactly what I was looking for. Piwik appears to be the industry standard alternative so going to get that loaded up and will jump into the log analysis after that.

+1 for Piwik without question.