Many stations are broadcasting digital, but not necessarily HDTV.
Digital is still a major improvement - no ghosts, no snow, just nice clean picture. Digital broadcasting still suffers some from multipath (the conditions that cause ghosting on analog sets). Instead of ghosts, the picture freezes and breaks up. The level of multipath to cause that to happen would still have to be pretty strong.
In chicago, for example, the classic over-the-air scenario is that viewers pretty much have to choose between channel 2 (CBS) and channel 5 (NBC) - if you aim for one, the other is pretty much unwatchable with ghosting and other interference. With Digital (channel 2.1 and 5.1) you can now watch both with clean pictures (there are some issues with channel 2, but in most areas around Chicago, this statement is true).
AVS Forum is a great source of info. Read the FAQs well before posting a question: if you think computer people get snippy about redundant questions, wait till you talk to the "serious" TV people

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Good Luck
Scott