It's no longer necessary to paginate for users, but content providers love it for advertising.
Common knowledge among content strategists in my work is that you paginate in order to increase advertising impressions. A slideshow with ten slides gets ten times the impressions as an article with ten photos. And an article with three pages gets … well, you get the idea.
In the old days, pagination was about bandwidth. And in the old days, people didn't know or want to scroll. But those days are long gone.
From UX Myths (with many studies cited):
Although people weren’t used to scrolling in the mid-nineties, nowadays
it’s absolutely natural to use the browser’s scrollbar. For a
continuous and lengthy content, like an article or a tutorial,
scrolling provides even better usability than slicing up the text to
several pages.
And Google is pushing the full-page version in its search results, essentially saying "full pages are better than paginations." Content Strategy blog Eating Elephant writes about it here: Google JUST SAYS NO to Overpagination.
Interestingly, however, multiple pages can be used to track engagement: if users exit on an article page, you can't tell how long they were there, but if they click through each page, you can track their time on each page and how far through the tunnel they've gone. Magazine's Online summarizes this nicely, based on original comments in Twist Image's article on multiples page trickery.
What to do…
In order to balance business needs for more ad impressions with user needs for the most pleasant experience, consider the following:
Put a "full article" link with pagination somewhere at the top as well as the bottom. (If you only include a "full article" link, you run the risk in some cases of the user believing they are only looking at an abstract, rather than the beginning of the article.
If employing responsive web design principals, serve paginated articles when download speeds will degrade the experience of a full article.
If and when you paginate, do clearly indicate at the top what page the user is on, in case they land there from search results or a link.
[From an in-house developer] If you want the advantages of pagination with a full-page experience, use progressive loading as you see on Facebook and Twitter (also called "infinite scroll," although in this case it's finite).
Mashable does a good job of paginating when it improves the experience and defaulting to one page otherwise. Here's a nicely paginated slideshow on pregnancy time lapse videos, and here's a nice full-page article on self-driving cars. Note that the slideshow loads an ad with each slide (often the same ad).
New York Times appears to have designed some flexibility into their system by making pagination beyond the first page a request string in the URL. That way, if they decide to change to full pages, the URLs don't break (I surmise). Anyway, NYTimes breaks into pages without feeling egregious.