As we move further into the era of cord-cutting, with streaming replacing cable TV, some of the options can get a bit confusing. HBO, for example, offers both HBO Go and HBO Now. Showtime has both a Showtime app and a Showtime Anytime app. Amazon Prime is also a popular service for streaming movies and shows, and we'll look at that option as well. In general, these services are trying to make themselves available on as many devices as possible.
HBO
Starting in 2011 could get HBO on your iPhone or iPad via the HBO Go (free) app if you already had cable service and subscribed to the HBO channel. You simply logged into the HBO Go app using the credentials you set up through your participating television provider or that you set up on hbogo.com. HBO Go also has an app for Apple TV, though not all cable services have made it available. Then in April 2015 HBO launched a standalone streaming service for $15/month via the HBO Now app (free). Cord cutters rejoiced. If you're interested, you can sign up for a 30-day free trial. It was announced at an Apple event and initially was just available on the iPhone, iPad, and Apple TV.
Showtime
Similarly, Showtime launched a Showtime Anytime app (free) in 2011 that let cable subscribers stream Showtime programming to an iPhone and iPad at no additional cost. The service came to Apple TV in 2014. Again, it entailed logging in with one's cable credentials. In July of 2015 Showtime launched its standalone service for the iPhone, iPad, and Apple TV via the Showtime app (free) for $11 per month. Showtime also offers a 30-day free trial.
Amazon Prime
I also wanted to mention Amazon Prime, since it's one of the better deals for cable cutters who want a service that offers unlimited streaming of movies and shows. For $99 per year, which is just slightly more than the $96 you'd pay for Netflix (at $8 per month), you also get free, two-day shipping on any Amazon purchases and free e-book lending and borrowing. The price for students is $49 per year.
You can stream video to your iPhone or iPad via the Amazon Video app (free). You can stream Amazon Prime video from your iPhone or iPad to your Apple TV via the AirPlay feature. There isn't yet an Amazon Video app for the Apple TV, though it's been rumored that Amazon is working on one.