TWC here did this two years ago. Gave us a free year of "rental" on the converter boxes, then went to like $2.99 a month per box after that.
The built-in digital tuner on my HD set still works though it only picks up the basic tier channels (local over the airs mostly). Sometimes a higher tier channel pops up for a little bit but then disappears again. Had NESN coming through for about a month once (sharper HD picture than through the box too), and the free previews of the EI package usually work also. The catch is the channels aren't mapped like they would be with a box, so they're on odd numbers like 8-12 and 34-135, and they occasionally change so you have to re-scan the dial to find them again.
Basically, if you want to watch anything more than the over-the-air local networks while being able to reliably find them on the same channel numbers every day, you need a converter box. But you probably don't need one for every TV in the house if they have a digital tuner built-in.