I grew up in the southern tips of the Appalachian Mts. This is where most everyone that is labeled a "hillbilly" lives. I have one of the thickest accents of any of the people I grew up with. It's because my parent's accents were so thick. When I went away for college it got cleaned up a little from being mixed with so many other accents. But when I go home, or even talk on the phone with my parents, I go into that southern drawl that people frequently say they can't understand. It definatley gets worse when I am excited or mad.
Examples:

(some already used)
Co-Cola not Coca-Cola
Coke means any soda drink. Then you have to specify which type of coke you want.
Anything that ends in -ing, now ends in -in'
I drawl out my words so slow and long that they sound weird and run together.
It is a buggy, not a shopping cart.
Milk is mee-ulk, two syllables. And generally any one syllable word is drawn into two.
It is totally a couch not a sofa.
They are tennis shoes not sneakers. I thought sneakers were less for sports than tennis shoes and were a different type of shoe.
It's "The Walmarts" instead of Walmart.
I "reackon" a lot of things (ie. I reackon it's gonna rain today)
"Over yonder" - I reackon he's over yonder somewhere.
Oh I know so many more but can't remember now. Maybe I'll come back with more later.