I use my PHP back-end to detect AJAX requests by checking for a value in $_SERVER[\'HTTP_X_REQUESTED_WITH\'].
This gives me a reliable detection, making
Regarding your last question: "Does it even matter, in these days?" This is a case by case question. If the ajax request is doing something that does not require security (e.g. loading latest stock quotes) then it really doesn't matter IMHO. If the request is loading information that should be secured (e.g. returning identifying information or doing something on the server) then you should treat it as such.
I personally don't use the server variables to know when something is an ajax request. Instead I just add a query parameter to the ajax call (e.g. http://domain.com/?ajax=true). If I need to secure the ajax call then I would use the same methods as securing a regular page request (using both client and server). As Lucas Oman pointed out, anything on the client side can be faked. Bottom line don't trust any request even if you think it is coming from your site or database. Always follow the mantra "filter input - escape output".