[CentOS] Apache attacks - you can't stop them, or can you?

So I have this nice, simple web server up running.  Its purpose is to 
allow me external testing with HIP, and to provide some files for 
external distribution.  Of course, there it is sitting on port 80 and 
the attacks are coming in per logwatch report.  Examples from the report 
include:

  Requests with error response codes
     404 Not Found
        //phpMyAdmin-2.5.1/scripts/setup.php: 1 Time(s)
        //phpMyAdmin-2.5.4/scripts/setup.php: 1 Time(s)
        //phpMyAdmin-2.5.5-pl1/scripts/setup.php: 1 Time(s)
        //phpMyAdmin-2.5.5-rc1/scripts/setup.php: 1 Time(s)
        //phpMyAdmin-2.5.5-rc2/scripts/setup.php: 1 Time(s)
        /muieblackcat: 1 Time(s)
        /myadmin/scripts/setup.php: 2 Time(s)
        /mysql-admin/scripts/setup.php: 1 Time(s)
        /mysql/scripts/setup.php: 1 Time(s)
        /mysqladmin/scripts/setup.php: 2 Time(s)
        /mysqlmanager/scripts/setup.php: 1 Time(s)

Now these are only a few, though I am probably not being hit as hard as 
others out there.

My question is:

Is there a way to shut this nonsense down?  Or because I am sending the 
404, I am doing all that is reasonable to do?

I am wondering that if this list starts getting long, that is a lot of 
logging and I probably don't need to log 404s?