Take a look at http://en.wikipedia.org/wiki/Z3_(computer). I think the early machines were not Turing complete in any practical sense (no looping instructions), though they were good for many calculations. Also, take a look at his monograph, "The Computing Universe", where he posits the possibility that the Universe is a kind of enormous computer, constantly computing its own existence. This was decades before Wolfram's similar book took up similar ideas.
As I wrote in my book "Bebop BYTES Back: An Unconventional Guide to Computers" (now sadly out of print):
In 1943, Zuse started work on a general-purpose relay computer called the Z4. Sadly, the original Z3 was destroyed by bombing in 1944 and therefore didn't survive the war (although a new Z3 was reconstructed in the 1960s). However, the Z4 did survive — in a cave in the Bavarian Alps — and by 1950 it was up and running in a Zurich bank. It is interesting to note that paper was in short supply in Germany during to the war, so instead of using paper tape, Zuse was obliged to punch holes in old movie film to store his programs and data. We may only speculate as to the films Zuse used for his hole-punching activities; for example, were any first-edition Marlene Dietrich classics on the list? (Marlene Dietrich fell out of favor with the Hitler regime when she emigrated to America in the early 1930s, but copies of her films would still have been around during the war.)
In my research on this, I think what was meant by "mechanical relays" is one mechanism that switched another mechanism, much like how a relay causes one electrical charge to switch another electrical charge.
@WillyK57: In 1943, the Z1... and 33 years later, the Z80 :-)
LOL But actually the Z1 was fully functional as far back as 1938 -- the year before the start of WWII and 5 years before the USA had anything worthwhile (on the digital computing front) up and running.
Hi Jeremy. Thanks for this article -- I've long been interested in Konrad Zuse. You say "It was able to execute instructions at 1 hertz off of a punched tape reader using only mechanical relays controlled by an electric motor."
I'm not sure what you mean by "mechanical relays" -- apart from the motor the whole Z1 computer was mechanical, including the memory. In fact, I believe that his next machine (the Z2) used electromechanical relays for the logic, but the memory was still mechanical.
Zuse was way ahead of his time. The Z1 was a binary floating-point machine. The amazing thing wa sthat he was completely unaware of things like Charles Babbage's Analytical Engine and Boolean Logic and suchlike -- he invented everything himself from first principles.