Hi jtg91, I'm new to this 3d stuff but it looks like your doing the Basic Human Modeling tutorial by Kurt. I just completed that tutorial myself and I had the same problem trying to union the arm to the body. both my body and arm dissappeared.
The problem for me was that my arm was not completely inserted into the body. There was a gap between part of my arm and the body (even though it looked inserted). Once I found that stray vertex and moved it into the body, the union worked perfectly. You just gotta make sure the etire edge of the arm is COMPLETELY inserted into the body. As Kurt instructed in the tutorial, increase the width of your border edges and you'll easily see if any parts are not fully inserted.
Even after you perform the union, you still have to go in and merge vertexes, so I agree with everyone else, that sometimes it's better just to marry up the two pieces of geometry, combine them, and then merge the vertexes.