[Trying to clear out the queue of draft posts here… I started writing this post in September of 2008 but never posted it for some reason!]
Thanks to Rod at Reasonable Deviations, I recently read about Curta calculators — amazing mechanical calculators that were manufactured from the 1940s to 1970s.
If you want to play with one, here’s a simulator that someone made. If would be even more fun to play with one in real life, of course, but I hear they are rather expensive now! I saw one in real life in a display case in the Princeton computer science department—but of course I didn’t get to play with it.
I also encourage you to go read Rod’s post, which includes a number of other links to information about these fascinating machines!
The Math Less Traveled 
Another incredibly sexy analog computer is the Phillips machine.
Wow, so it is!
Pretty cool post. I just came by your site and wanted to say
that I have really liked reading your posts. Anyway
I’ll be subscribing to your feed and I hope you post again soon!
Just checked out the Phillips Machine. Incredible!