If I put a ping pong ball in a vacuum, would it pop? If I put a ping pong ball in a vacuum, would it pop?  If so, at what point would it happen?  Any standard table ping pong ball is acceptable.
 A: Probably not - but without knowing the details of the specific ping-pong ball it's hard to tell.
There may be an international standard for ping-pong balls who would be happy to tell you!
The interesting part about the question is scaling laws. In a vacuum there is a pressure of one atmosphere (15psi or 10tons/m^2) acting outward on the inside of the ball.    
BUT there aren't all that many square meters (or even square inches) on a ping-pong ball so the actual force is really quite low.  
A sphere is a good shape for resisting this force, the most likely failure is the glue seam that holds the two halves together.  And a ball has to survive the force of being hit pretty hard by a bat so the glue line is reasonably strong.
A: The answer to your question is "no".  A quick web search for "ping-pong vacuum" yields a wealth of experimental evidence, in the form of articles with photographs about cannons that operate by putting ping-pong balls in vacuum and selectively releasing the vacuum.  
Here are some videos of demonstrations.  Note that the balls don't pop before being fired.
