[mh-cx]

Agree. The Z3 is exhibited at the Deutsches Museum in Munich:

http://www.deutsches-museum.de/en/exhibitions/communication/...

Here's the Z3 in action (German only, try subtitles):

https://www.youtube.com/watch?v=aUXnhVrT4CI

[jdietrich]

The Deutsches Technikmuseum in Berlin has a reconstruction of the Z1.

http://www.sdtb.de/Mathematics-and-Computer-Science.1256.0.h...

[c7h]

I can highly recommend a visit there. Not only you can see an original Z4 and a replica of the Z3, but also lot's of more science and history related exhibitions. Don't miss the Enigma!

[ptaipale]

Among the more impressive specimens, you can also see an A4 rocket (better known as V2).

[lorenzhs]

Z22 is at ZKM in Karlsruhe, but Deutsches Museum has a whole department on Z3 and related machines. I can highly recommend it to anyone interested in (very) early computers!