Hi Kazz,
Looks like the native Trillium cuneatum.* Wonderful plants!
http://2bnthewild.com/plants/H16.htm
It looks like they are in a pot.* I was relieved when you said you own those woods as it's not a good thing to dig plants from the wild, especially native plants.* In many states it's illegal to dig native plants from the wild.* Here's a list of more native wildflowers you can plant to enhance your Kentucky woods.
http://www.daviessaudubon.org/wildflowers.html
There are many varieties of Trillium, most with solid green leaves and flower colors that range from maroon to red to pink to white to yellow.* I get mine from a native plant nursery in Maryland.* Here's a gallery that will make you drool.* :shock:*
http://www.goldsword.com/sfarmer/Trillium/gallery.html
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.