The statistics module of the drupal cms is well known bottleneck that causes most of the high loads of Drupal system. It is by default disabled in Drupal7 but if you're using drupal 6 you must disable it at once.
If you need it and you cant disable there are no real alternatives on drupal 7 may be something better will be included in the upcoming drupal 8.
Things you can do with drupal 6 is to go /admin/by-module > Access log settings and disable Access log and Count content views. This is at least will let you create things like most popular block and things like that.
Also another bottleneck is also xmlsitemap creation and submission to search engines, disable Prefetch URL aliases during sitemap generation which will cause heavy load on your server.
Furthermore, increase Minimum sitemap lifetime to higher number than one hour.
There are other mentioned alternatives regarding using Google analytics which i found it difficult and it didn't work for me.