What should I use to analyze conversions, web traffic etc?

I’m looking for some sort of stasticial package that will be able to track and analyze visitors habits on my website (without messing with the URLs of the website).
For example I’d like to know
– conversions on Adsense campaings
– how people move throughout my website from page to page
– The conversion ratio from specific traffic from a single web page or search engine keyword traffic.
Any recommendations

Original post by mrsolutions