Piwik is an open source, self hosted version of Google Analytics. It's got an active community backing it so there is a lot of plugins and customizations for it too. It's not often talked about but it's a solid solution.
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Google Analytics, AwStats and your web hosting logs along with the program which tells you the latest visitors that have accessed your site, also accessible from hosting panel, can everyday tell you how your website is doing online. The first option, Google Keyword which I believe you are referring to the AdWords keyword suggestion tool is primarily used to spot the best keywords, rather than discovering how many people have visited a site.
Alexa seems to be getting better day by day, compared with the past, and the stats they offer for websites in most cases solely match their stats on Google, the higher positions, the lower numbers that seem logical. You are recommended to use a combination of tools rather than trying to find only the best or one single program to learn more about your overall website's popularly online.
If you don't mind giving google your data... which they will then profit on, then they are by far the most customisable easy to use solution.
If you want to keep your data private awstats is simple to use and setup. AWstats is also good.
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