I occasionally come across pages where some Javascript is included via a PHP file:
Absolutely none, IMHO. I use a js framework that I wrote to handle the setting of whatever server-side variables I need to have access to. It is essentially the same as embedding PHP in JavaScript, but much less ambiguous. Using this method allows you to also completely separate server-side logic and html away from javascript. This results in much cleaner, more organized and lowly-coupled modular code.
You could do something like this in your html:
And then do something like this in your js:
if (registry.myInt === 1) {
alert(registry.myString);
}