Does this C binary search tree have memory leaks?
The code looks nice.  Just a few comments:  

In new_node, your word-copying is wrong as you use sizeof(nword) where
nword is a pointer.  Using sizeof on a pointer gives only the size of the
pointer itself, not the size of what it points to.  try it with some long
words.  Your word copying could either use strdup or if you don't have that,
write your own.

In main, set n to NULL before using it.

There are no checks for malloc failure.  It is good practice to check, but the
only thing one can do is often to exit.

It is best to avoid leading underscore on identifiers (they are reserved).  And it is generally better to use explicit braces around statements even when strictly unnecessary.