The Drupal statistics module keeps track of how many times a node has been viewed. The statistics module is an optional core module so just turn it on and it will start keeping track of your node views. It stores the data in the node_counter table and keeps track of daily views and total views.

If you are using the "Today's popular content" and "Popular content" blocks from the views module (like I am in the left sidebar), these blocks get their data from the node_counter data.

The problem with these statistics is that they also include views by admins and the author of the nodes, so it's not very accurate. Also, even if you aren't the admin or node author, if you go to a page and keep reloading the page, the node count keeps incrementing.

The way to improve your statistics is to install the Statistics Advanced Settings module.

1) Download module
2) Untar
3) Put in sites/all/modules/statistics_advanced
4) Turn on module via admin/build/modules
5) Configure settings via admin/reports/settings/advanced

You can ignore search engine crawls by installing Browscap module and checking the box on the settings (in 5) to ignore these.