I write for and read a niche publication related to an obscure hobby of mine (related to model trains) and it actually sells very well and they still pay well for contributions. Mostly because the target audience is retirees who are of a generation that are used to and comfortable reading the printed page, and are happy to pay for it. Many of these people also supplement their subscription with online forum discussions, which has changed the nature of the magazine. The primary focus is on lengthy how-to articles that people would not normally compile for free and post online due to the time and effort involved, but are happy to put into print because they (and I) are being paid for it. Club announcements and updates and stuff are less needed thanks to online forums.
The one thing the magazine has not done is embraced a digital version and made their archives available digitally. One magazine that has done this to great effect is Model Railroader. Rather than collect stacks of back issues, you can now get the whole set online or on discs. One of the main issues depends on what the original contract with the writers looked like. If it did not have a 'and all future media' type clause, you would have to seek individual permission from each contributor to make the back issues available digitally. That has been one of the things holding back the particular magazine I write for. I myself am all in favor of making back issues available digitally. At the very least they could sell a digital edition beginning with new issues, with a new contract for the writers that includes it.
As far as mainstream periodicals, I occasionally like to pick up a Wall Street Journal or a New York Times when at an Airport, but 99.9% of my current news intake happens online these days. Financial Times of London is a good one, but again can be had online.
what I do read exclusively in printed form is books. I just like them, and I like to keep the best ones for re-reading later. Mine will be among the last generation to prefer this most likely.