On Saturday, September 1, 2007 7:54:34 PM UTC-4, wrote:
I don't know what this is but wondering if anybody knows.

At the top of my closet doors on each door there is a ball bearing
that keeps the door shut
when you close it. Below the ball bearing in the door is a spring.

Does anybody know what this is called and where I can get a
replacement.

Use a pair of pliers to slightly narrow the opening on the top (only) of the round cylindrical fitting that screws into housing that's fixed in the top of the door. You don't want to pinch the bottom as then it won't screw back into the door and or the ball won't fit back into fitting.