They are all the rage, right now, as are the series of novels that continue a single story, which are more rightfully serials.
The Millenium Trilogy
Fifty Shades ... of Gray ... Darker ... Freed
You can blame these megasellers for the fashion, if you like, but authors have been writing sequels since before Alice Through the Looking Glass, and once a sequel to the sequel is written, you've got yourself a series.
Or a serial. A sort of paper or eBook version of "Dynasty" or "Coronation Street." You can blame TV for that, perhaps. But it can work very well indeed -- think Shayne Parkinson's bestselling "Promises to Keep" serial.
But how easy is it to bring off a trilogy or a series or a serial? If the second (or third, or tenth) book is a dud, the first book, no matter how brilliant and well-reviewed, is going to suffer reader backlash. The writer would have been wise to stop at book one.
Often it is the bridging -- or lack of bridging -- from one book to the next that fails. Too much repetition of what went before, and not only are the previous book or books spoiled for the new reader, but the story is so stalled that it is really easy to put the book or Kindle down. But, if the writer leaps right into the next book without bothering with any echoes of what went before -- not bothering to describe the major characters again, for instance -- the new reader feels alienated. It's like walking into a room halfway through a conversation, which might be fascinating for those who have been there all along, but is baffling to the newcomer.
Hunger Games is a prime example of how to get it right. The first book sets the scene -- reality TV gone crazy -- and introduces the major characters. There's a satisfying resolution. It feels like a complete novel. So it must have been quite a challenge to pick up the setting and story again.
Collins, deftly, does it through character development. Her protagonist Katniss has become wise and cynical, and reacts to tension quite differently. We watch her change from bewildered participant in a game that is controlled from outside, into a budding terrorist, subject to other controls, and finally the resolute woman who takes fate into her own hands. And that final, final resolution, in the third book, Mockingjay, is a total shock. It's a book that makes you think for a long time after you have finished, and makes you want to start reading the series all over again.
Well worth studying.