The kids watch Netflix or YouTube Kids. My wife and I mostly watch Netflix, Hulu or Amazon Prime (mostly Netflix) on our Roku. We have had DirecTV for over 3 years because when we moved in, it was just one more utility that we needed to transfer over.
However, as time went on, we realized that our $75 (and growing!) cable bill really wasn't worth it anymore. No one watched the channels it gave us. I mostly used it to watch the evening news, record SNL and watch our local sports teams.
After a ton of research, I decided to dump cable and live the cable TV cord-cutters lifestyle. To be honest, it really couldn't have gone any smoother. The kids don't notice a difference at all - they never watched it in the first place. With the DTV antenna I bought (I settled on the Mohu 50), I get crystal-clear reception from all our local Pittsburgh affiliate stations (CBS, NBC, ABC & Fox). This is even with my house being close to 50 miles away from all their broadcast station transmitters.
Replacing my beloved local sports was a little more difficult, but I found an online service called ExpressVPN. These guys saved my day with their service that give my home an IP address that is not registered to my local area. This makes certain that I wouldn't be subject to blackout restrictions when watching the professional Pirates (MLB) or Penguins (NHL) games from my home.