The letter 'z' seems to freak out native English speaking learners of German. Many develop an impression that it's different and foreign and hard and therefore give up on it quickly. But mispronunciation of a common consonant is one of those clues a native speaker will pick up on immediately that you perhaps need them to switch to English on your behalf. Even if that's not true.
Giving up early on the 'z' is a shame. The sound itself is one that we native English speakers use frequently — just not word-initially, like it can occur in German.
Here's where you use it in English:
...just to name a few proper nouns. A few of those seem Russian in origin (Trotsky, Yeltsin) -- maybe the acceptable pronunciation of Czar (though we prefer Tsar) has wrought havoc on Americans' confidence in pronunciation of German word-initial Z sounds.
And, if you've ever beatboxed the intro to the very awesome Take The Money and Run by the Steve Miller Band, you're rocking the German Z as an initial consonant without even thinking about it on those two punctuating cymbal hits (it happens at 3 seconds and 6 seconds in this clip). Bop around the house or on your way to the bus a few days and you'll be ready to apply that sound to the front of all those German words starting with Z.
By the way, that German Z is sometimes supplanted by a C in old-timey writings: Centrum instead of Zentrumfor the Innenstadt. The sound is the same in those cases, but not in the hundredth part of the Euro currency: that is a Cent, pronounced the same as in English.
Just because it's alphabetically the last letter doesn't mean you can slack off on that sound. It has relegated the 'y' on the German keyboard down to Left Pinkyville for good reason. Give it the respect it deserves, and you'll get more, too.