(Mike Blake/Reuters)

In the old days of video streaming — that is, not so long ago — consumers could cut the cable cord and subscribe to one or two services, enjoying a vast array of movies and television programming at a rate far less than the monster cable bill.

It’s not so simple anymore.

Disney, the juggernaut behind ESPN, Pixar, Marvel and the recent additions to the Star Wars franchise, shook the entertainment world this week with an announcement that it would remove many of its offerings from Netflix. The company said it would create a service — or multiple services — for its films and shows, and another for ESPN.

As a result, a Netflix user who enjoyed access to Disney content — plus all of Netflix’s other content — on one site may have to turn to three or more sites to get it all. “It’s all in discussion,” said Disney chief executive Bob Iger.

It is the most recent example of how the move toward streaming — though consumers have been demanding it for years — is proving to be a more fragmented experience than many have anticipated. Entertainment companies are now running services with increasingly narrow offerings, looking to hit consumers up for more subscription revenue wherever possible.

“I worry that we’ll be going down yet another rabbit hole where exclusivity will take over and I’ll ultimately end up paying more for less,” said Brett Hatten, a father of two toddlers from Chicago who already pays for six streaming services. “I don’t want to end up in a place where you have to subscribe to a bunch of different fiefdoms.”

The shift is breaking down popular expectations in the entertainment world. For a half-century, for instance, viewers have expected to see shows on CBS broadcast free over the air on their TV. But this year, the network is launching highly anticipated shows such as the sequel to “The Good Wife” and a new “Star Trek” series only on its online service, marking yet another service people may need to subscribe to. CBS announced a separate sports streaming service this week.

CBS sees this as a way to court specific audiences. “To succeed, you need a great core and content that only you have,” Marc DeBevoise, the president of CBS Interactive, said of the network’s streaming service, CBS All Access.

The original programs, for example, specifically court an audience interested in prestige dramas. “These are not for a big, broad audience,” he said.

And the plethora of television options is changing consumer behaviors in still other ways, leading many viewers to hopscotch between services, subscribing to HBO for a few months to watch “Game of Thrones,” then moving to Showtime to take in “The Affair,” before joining yet another service for an eight-episode binge.

“I happily subscribe to Netflix, Hulu and Amazon Prime, which all have a wide selection of shows and movies. But when I consider other streaming services, the costs add up,” said Diana Urban, a 30-year-old marketing manager and fiction author in Boston. She signs up for HBO Now during “Game of Thrones” season, when she also catches up on “Veep” and a few other shows. “Paying $15 a month indefinitely for only four shows isn’t worth it,” she said.

Streaming services such as Netflix, Hulu and Amazon Prime, which offers a video library along with its other features, such as free two-day shipping, took off in part because they promised a convenient, cheaper alternative to cable. (Amazon chief executive Jeffrey P. Bezos owns The Washington Post.)

Cable companies are bound to distribution deals from network conglomerates, including Disney, which require cable firms to pair their most popular channels with less popular ones. As cable-bill prices continued to climb every year, however, consumers balked at paying more for content that they didn’t want and some decided to turn to streaming sites.

The shift has prompted cable companies to explore smaller cable packages that cut the bloat. But for many customers, making their own bundles of streaming services has proved appealing. Those not interested in live sports — which contributes a lot to the cost of a cable package — can easily get news, movies or sitcoms from Netflix or Hulu without having to buy a preset bundle. (Or they can get just the opposite, in the case of ESPN’s upcoming stand-alone service.)

That’s provided consumers with a lot of choice, said John Bergmayer, senior counsel at the consumer advocacy group Public Knowledge.

“The stranglehold of cable isn’t broken yet — for most people it’s hard to cut the cord — but these are all really good signs,” he said.

But it’s clear from viewers that the cost per service is a growing concern. “The current influx of these subscription-based plans is saturating the market,” said Jamie O’Dell, 35, a food safety program manager from Albany, N.Y. “We do not need more options for streaming services,” she said. “We need less.”

About 21 percent of American video viewers pay for multiple streaming-video on-demand services, according to the market research company GfK. That number has grown by roughly one-third for the past three years.

Big streaming services such as Netflix provide subscribers content from many sources. But many others are now getting into the game. At least six networks have launched services, with subscription fees ranging from $6 to $15 per month. Many of those already offer their shows in some way through existing services.

Now, consumers may find that shows and films they used to be able to access on broader services such as Netflix are pulled out for a separate service. The cost and mental effort of managing multiple services may be starting to prove nettlesome.

“I just don’t want another subscription bill I have to pay,” said Erin Thompson, a mother of four from North Tonawanda, N.Y.

Justifying the hassle of managing another service also puts pressure on Disney and rivals, creating a different kind of relationship with its fans, analysts say.

The company will have a more direct line to consumers but will also have to deal with complaints, for example, about the quality and reliability of their streams.

The appeal of streaming will prompt many more companies to launch their own video streaming services, said Brian Wieser, senior research analyst at Pivotal Research Group. “It’s inevitable [there will be] more direct-to-consumer offerings as time progresses.”