I think the answer to my question depends on where you are located geographically, including the size of the metropolitan area in which you live. I'd say small town papers are not dying, mainly because their readers seek more local versus national news. In areas where there is a greater mix of readers, I'd say newspapers like the NYT or Washington Post are on borrowed time.
Why? Simple. Most people below the age of thirty get most of their news online. And, big newspapers generally have their full print available that way, for free. Also, I suspect most of those in that age group are only looking for "headline" news anyway, and may never take the time to actually read anything online from a newspaper's site.
Magazines seem to be going the same way, especially national publications such as Time or Newsweek. As advertisements decline, so do the number of pages in the magazine, and then "woof" it's gone for good.
More tightly focused magazines such as those related to sports, outdoor activities, tourism, and hobbies may not be seeing as much trouble with circulation. Certainly I hope that circulation of Army Engineer magazine does not decline. In that regard, guess I'd better get back to work on the next issue!