Veronika

Hungarian pronunciation: VE-ro-ni-kaw. [noted -ed]

Pronounced veh-RON-ee-kah (short) in Croatian. [noted -ed]

In Czech and Hungarian, at least, the name would be accented on the first syllable (as is everything else in these languages, though in Czech there is some dialectal variation). In Hungarian the pronunciation would be (approximately) VAR-o-nee-ka. I knew a Hungarian-born woman with this name. She said the usual nickname was Veron (pronounced VAR-on).

So now I found links that tell about the Russian pronunciation of Veronika. (http://www.geocities.com/Colosseum/Track/7635/names.html) - in English
(http://www.masterrussian.com/aa031001a.shtml) - in English
+ Russian wikipedia, where you can see easily see the stress mark. In the brackets there is information about stressing "in west". (http://ru.wikipedia.org/wiki/%D0%92%D0%B5%D1%80%D0%BE%D0%BD%D0%B8%D0%BA%D0%B0_%28%D0%B8%D0%BC%D1%8F%29)

My mother-in-law's name. She is German, and she pronounces it "Ver-OH-nee-ka".

I'm pretty sure that Veronika is pronounced Vye-ro-NEE-kah (at least in Russian), not Ve-RO-nee-kah. [noted -ed]

ToveTer: It is really pronounced Ve-RAW-nee-kah.

Listen to the German pronunciation of Veronika here:
http://www.nordicnames.de/Aussprache.html.