Not all cable companies make their digital channels accessible without a converter box, however, no matter what capabilities your TV has. For example, Comcast (at least in Massachusetts where I lived) requires a converter box for ALL channels other than analogue (SD) versions of broadcast channels. That's all you'll get if you just plug the coax from the wall into your TV, no matter what kind of TV it is.
Same here. Before Comcast went all digital, you could get several broadcast and cable channels in digital with the built-in digital tuner in your TV (although the channel numbers were weird... TWC is channel 36 under normal circumstances, but in digital it was channel 86.4)
At the time, a buddy of mine had a digital box in his living room (full access to all digital channels in whatever package he had) while his kids' rooms had the standard plugged-straight-into-the-wall connection with the built-in digital tuner (the few select digital channels that Comcast offered). He used to tell me that the digital picture quality in his kids' rooms was MUCH better than what he was getting with the stupid box in his living room. And now that I'm having to deal with a box, I agree with him 100%.
I wish they'd go back to the way it was.