Chuck,
Need more information to answer your question directly. There are many
reasons why this is happening and the vast majority of them have nothing to
do with Word. But here's a start...
1. The first thing I'd try is closing all running Office applications, then
trying again.
2. Then, assuming you're running a windows system, go to the task manager
(CTRL-ALT-DELETE > Task Manager), and under the processes tab, see if
MSWord.exe is running after you clicked the attachment. If so, click End
Process and try again (this actually is more common with opening pdf's, but
I've seen it happens with docs).
3. If still nothing is happening, it could be a number of things, including
your system's association for .doc files. But, before you do anything else,
your best bet is to reboot, as that returns your computer to a relatively
clean condition and clears the RAM of anything that could be causing the
problem.