There are already logs for httpd (Apache) for both successful access and errors. Normally they are kept in the /var/log/httpd directory but this can be changed in your httpd.conf file.
<VirtualHost 10.1.2.3>
ServerAdmin webmaster@host.foo.com
DocumentRoot /www/docs/host.foo.com
ServerName host.foo.com
ErrorLog logs/host.foo.com-error_log
TransferLog logs/host.foo.com-access_log
</VirtualHost>
I use separate sets of log files for each domain on the server.
hat you are probably looking for is something like "logwatch". It monitors your logs and sends you a report daily for attempted hacks, login failures, web site failures etc. Google logwatch and you will see several links.