theres no real advantage, its just used to symbolize that its a file thats commonly included, like a file with just a bunch of function definitions in it.
do be carefull though, like said above, if you goto yourwebsite.org/includes/database_connection.inc
most likely the file be output as plain text unless you configure apache to parse .inc files as php code, or preferable just spit out a permission denied message.
personally, i use filename.inc.php
that way no matter the config of the server, it will at least be parsed as php code, and not output as plain text.
