I am searching for an old friend I used to know that lives somewhere
in Hungary.  I have her name and her old address.  Is there a people
search service that can find a person living in Hungary?

Try this, or wait for a real researcher :)

http://www.matav.hu/tudakozo/index_e.html

i've tried that, its more of a "white pages" than a search service. 
i'm specifically looking for a pay-per-service that will do the work
for me.  the people finders that I seem to find on the web are all for
just the USA.

thanks though! :)

Try this, they're in the people search business, I think:
http://www.janda.hu/

Other links:
http://detektiv.lap.hu/ > Magánnyomozók (lower right on the page)