Well you need a turner somewhere in the mix, and the type of tuner depends on the type of cable signal. If its unscrambled QAM then you need that type of turner, if its ATSC (like off the air broadcasts) then you need a ATSC tuner. Most new HDTV digital televisions support both of these standards.
I use this USB device
this for watching Off the Air TV and Clear QAM (which is used in some cable TV systems). It still requires a computer (or laptop in my case).
Here is the Amazon link
I'm sure you could also get a stand alone tuner as long as it interfaced to the monitor for both video and sound (likely using HDMI cable). I find HDMI to be flaky at times however.