It really depends on how they are filled. Most places I've been to don't take a whole lot of care in filling them to preserve the contents, so I try to drink them the same day or on day two. If they're filled correctly (like you would bottle from a keg), in theory they could last as long as any other bottle of beer. But finding places near me that know how to do that, or care to, is pretty unusual. Most places here seem to have one or two bartenders that know what they're doing, and if they're not there its a crap shoot. I even had a guy a while back fill a pitcher and then pour it into the growler and I about ****.
And of course, once they're opened they should be finished that day.