There are a couple of threads on that.
Here's
one on general cutting of cable.
Are you thinking of going with a full-on HTPC?
Regardless, you probably want to look into XBMC (now called, unfortunately, Kodi). The current favorite budget box for XBMC seems to be the FireTV. Don't give up on live sports, as Sportsdevil pretty much gets you whatever you want (though not always in HiDef).
So basically you'd need to get a FireTV then follow the
instructions on installing XBMC on it. From there, the sky's the limit as to what you can do.