As of right now, there're a few ways to stream content from HBO. You can subscribe to HBO via your cable provider and use HBO Go, you can buy episodes from iTunes, Amazon, Google Play or somewhere similar (usually well after they air live), or you can watch older HBO content via Amazon Prime Instant Video.
Next month things will change. In early April (in time for the April 12th premier of the new season of Game of Thrones) HBO will introduce a stand-alone subscription service — no cable subscription required — called HBO Now. It'll cost $15/month, which is a few bucks more than what the service costs via most cable providers. HBO says you'll get all its original programming as well as movies via HBO Now.
This is something a lot of my friends have been clamoring for; a way to get current HBO series without a cable subscription. Until now these friends have turned to illegitimate ways to watch HBO content. It's not that these people don't want to pay; its that there has been no legitimate way for them to pay for HBO content when it first airs.
But there's a catch. A big hairy fly in the ointment. HBO Now will be exclusive to Apple devices (and PC) for the first 3 months. That means if you have a Roku, Amazon Fire TV, Chromecast, smart TV, or a gaming console that you use to stream content you're going to be looking to torrents for your Game of Thrones fix again this season.
This seems like a terrible choice for HBO to make, but presumably Apple backed up to HBO HQ with a dump truck full of money in order to buy this exclusivity period in an attempt to sell a bunch of Apple TVs. The one silver lining is that Apple has (finally!) reduced the cost of the Apple TV from $99 to $69. Considering the hardware hasn't been updated in two years a price drop is long overdue. The $69 price has already kicked in.
If you're an Apple person you'll be glad to know that you can get a month of HBO Now for free if you subscribe in April.