Word for "taking advantage of non-public resource"?

A freeloader is someone who exploits opportunities to get things for free. It can refer to any resource, such as time or space, but is most commonly applied to food, drink, and intoxicants.

I agree with Jon that freeloader would probably be the most common term, particularly in the US.

The literal definition of "scrounger" in the international English world would also qualify:

informal , derogatory A person who borrows from or lives off others

and a similar, more peculiarly Australian term is "Bludger".

Though it's worth noting that in the US the term "scrounger" also has a less derogatory meaning:

A cleverly resourceful person who finds and procures items for a specific purpose

I suspect that this secondary meaning probably stems from the role of a "scrounger" in POW camps during WW II. I've seen the term used in a number of history books which I don't have references to at the moment, but you can refer to, for instance, James Garner's character in the movie The Great Escape. Because of that dual meaning I'd probably be inclined to go more for "freeloader" which is universally understood and is universally negative, though in my own patch of Australia I suspect that "bludger" would be more commonly used.

As Tanninah noted "parasite" is another possibility, "advantage taker" is another term that I've heard used (but it's clumsier and obviously less concise than a single word), and in politics down here another expression has gained some currency recently; "lifters and leaners" with "leaners" being the type of people who take advantage of the work of others in the way described in the question.

In addition to "freeloader" the term "parasite" is certainly appropriate.

You can find other synonyms here http://www.thesaurus.com/browse/parasite if you prefer some more colorful terms. :)