The Curta Mechanical Calculator
vcalc.net
vcalc.net
But nowadays I think you can probably make things quite a bit smaller, even using conventional machining processes.
I'm a huge fan of flight computers too - they're basically a circular slide rule with common units marked. A lot of people don't use them regularly now that we have electronic calculators, but an E6B never runs out of batteries in midair. They're very easy for quick conversions once you get the hang of it.
ASA makes a nice one in aluminum that I really like: http://www.amazon.com/ASA-E6B-Metal-Flight-Computer/dp/B003Z...
And while we are at it, where are replicas of the Antikythera mechanism?
Heck, even a good slide rule would be nice. Think Geek had a slide rule for sale a few years ago and I bought a couple, but they were poor quality.
There are other gizmos that would be much easier to build. Like you say, slide rules are cool.
And some of the other mechanical computers would probably be easy enough to make:
http://www.computinghistory.org.uk/det/6717/Arithmometer:%20...
http://history-computer.com/MechanicalCalculators/Pioneers/M...
http://lecture.eingang.org/pascaline.html
https://calculating.wordpress.com/2011/11/23/calculators-for...
Some of these would work as papercraft. Someone creating a nice set of PDFs could probably make a bit of passive income.
It did not occur to me to look Curta calculator up- they sure do look to be worth obsessing about :)