I can recommend stats counter, and I have a Google analytic account, but my advice wouldn't be to stick to just one tool or software to monitor your website traffic.
If your hosting company offers server stats like Awstats then I would reommend using that - this updates every 24 hours but gives you good information on which search engines are visiting your site and pages and how regularly.
Top it off with something like stats counter which will give you live visitors, but go for unique visitors rather than hits as this is inaccurate.
It is vital that everyone has a statistical application, be it server end or via a webcounter site. I found out that I was getting a lot of traffic on one page, but they were only staying on the page for 15 seconds and then leaving the site..
After visiting this page I found the links weren't working (doh!) and the visitors were getting directed to a 404 error page! Without the stats I would not have known, and would of continued to loose traffic to a competitor.