It all depends on the store. Typically Target, Kohls, and other stores like that with just "good" deals are a few hours before.
Best Buy,
Walmart, Circuit City, will have people that go over right after, or sometimes even before Thanksgiving dinner. Some will bring tents, others just bring chairs and blankets. A few years ago at Best Buy on the way into the store there was a pile of tarps, tents, and camp chairs that people had left once the doors opened.
Some locations allow this, others will kick you off property until a certain time. It all depends on the store's physical location and the manager. I know that most of the amazing door busters at Best Buy are usually spoken for well before the store opens. I heard last year that the good tv deals at some stores were all accounted for people wise by midnight. Meaning that enough people in line wanted to buy the tv that anyone getting in line after them wouldn't have gotten it.
I have been at stores that bring around coffee and donuts for free while you are waiting, are very organized and orderly inside the store, and others where they have no clue, and its a mad dash for everything. It all depends on what item you want and where you go.