<p>Is it possible to call a COM API from Java (specifically the HP/Mercury Quality Center OTA API)? If so, what's the best way?</p>

<p>Is something like JACOB appropriate?</p>

<p>Code fragments would be helpful for the basics :-)</p>

jacob : yes,
http://sourceforge.net/projects/jacob-project/
is an active project that will suite your purpose pretty well.
you can see multiple examples :
http://jacob-project.wiki.sourceforge.net/Event+Callbacks
but if you want something that is more tested and are willing to pay money, then go for
http://www.nevaobject.com/_docs/_java2com/java2com.htm
.