Sling Media, not to be mistaken for Sling TV (which licenses the name to offer a separate service), produces a series of set-top boxes called Slingboxes capable of taking what's on your TV and streaming it to your mobile device. From there you can flip through channels using a virtual remote control regardless of whether you're on Wi-Fi or a cellular connection.
In addition to a Slingbox, you need the corresponding Android app to get everything to work. There's a separate version for phones and tablets, both of which cost $15. Except now Sling Media has produced a free version of each.
SlingPlayer Free for phones
SlingPlayer Free for tablets
Judging from the comments, it looks like the free versions don't require spending money to get off the ground. *That said, the Play Store page does list in-app purchases priced at $15 per item. That means Sling Media probably wants your money somewhere down the line. Still, no harm in giving the new apps a shot.