Chances are that most if not all of your scripts need database access to operate, which gives you two options: write database connection code into each of your scripts, or write it into just one script and link all your pages to that one. It is easy to place files outside of your public web directory, which means it is much easier to place all connection code into one file then place it in a secure location. If you place your connection code into each file, you are increasing the likelihood of your connection details getting out - all it would take is one page to be hacked.
There is, however, a third option that can sometimes be better: placing your connection details inside your php.ini file. If you do not supply connection details to mysql_connect(), PHP will use the values set in your php.ini file, which means you do not need to store your username and password information in your scripts any more. At first this might sound perfect, but it has major security implications of its own:
Anyone with access to your php.ini can read the values direct from the file
Anyone with the ability to put scripts on your server can use the ini_get() function to read the value from your php.ini file
If you firmly believe you are safe from these two, go ahead and use your php.ini file