Not having camped back east, I don't know exactly what you might hear, but out here I've heard:

1) deer footsteps - pretty loud and solid, depending on what the ground is like of course

2) wind blowing leaves and stuff - sounds like something creeping along if your imagination is overactive

3) rodents moving through leaves - see above

4) owls hooting

5) birds/rodents chirping or squeaking

A friend heard a mountain lion screaming repeatedly near her camp; it eventually unnerved her enough that she packed up and rode back home on her bike (she'd ridden out to camp for the night at Point Reyes). That's probably pretty rare.

I recommend getting some good (comfortable) earplugs. That way you can ignore all those things that make your imagination work overtime. Works for me!