When we cut the cord several years ago, I connected an old laptop to the TV via HDMI. I installed Kodi (formerly XBMC) and hooked up a 3TB external drive and a cheap USB TV tuner (HDHR w/ 2 tuners). We control Kodi and the laptop with a Media Center remote control, and also use a wireless keyboard. Now, all live OTA TV is routed through the TV tuner into the laptop and is recorded on the external drive. This enables all the standard DVR functionality like pausing live TV, recording 1 channel while watching another, skipping commercials, etc. Just using free software and some hardware I already had lying around.
Kodi also provides a free EPG (electronic program guide) and scheduling GUI which works great. With 3TB of storage, we record tons of OTA HD programming (with 5.1 sound) and never come close to capacity. The external drive also contains our entire collection of about 150 movies (ripped from DVDs), our entire MP3 collection (ripped from CDs), digital photos, home movies, etc, all of which is nicely organized and played via Kodi. All our old DVDs and CDs are stored in a box somewhere.
There are also thousands of 3rd-party add-ons for Kodi that open up the entire universe of internet streaming. Some of these are quite obviously accessing illegal content, so we stick to the official Kodi add-ons that only access legitimate and reliable streaming sources. Still tons of great free content, including traditional cable programming, much of which is not available via Netflix and Amazon.
If you have an old PC or laptop lying around, and you're a tech-savvy DIYer, this is a great and fun alternative to collecting a bunch of new hardware (Roku, TiVo, etc). The USB tuner was around $35 and the MCE remote was $15. We already had everything else (laptop and external drive); plus there's no ongoing subscription costs. IMHO, Kodi is a must-have for serious cable-cutters.