You can download raw access logs through your cPanel account.
Login to your account at www.yourdomain.com/cpanel, then select 'Raw Access Logs' under 'Stats/Logs'. Raw Access Logs allow you to see who has accessed your site without the use of graphs, charts or other graphics. You can use the Raw Access Logs menu to download a zipped version of the server's access log for your site. This can be very useful when you need to see who is accessing your site quickly.