Mammoth Cave is believed to be the world's largest cave. It lies in Kentucky's karst region, with lots of caves that may or may not be connected to one another somehow.
The other cave entrances I've seen in Mammoth Cave NP are gated off. This one, marked #205 by the Department of the Interior, was very much open. It is easily visible from a stream crossing on the Sal Hollow Trail, about a quarter mile east of Sal Hallow. I don't know whether it connects up with the main cave, or with any other.
A look inside the cave entrance is here
It is against park regulations to enter a cave without a permit.
Photo taken November 2008.