I've always heard that way-back-when, the simplest way to rewind a car's odometer was to drive backwards (at least in some models). Is this true? Did those manufacturers miss such an obvious gaming method?
Yes, older cars used mechanical odometers, which go forward or backwards, depending on which way the gears are turned. Modern cars use electronic odometers. I couldn't find anything indicating over what time period this changed. It was well before my time behind the wheel, though.
I also found a January 1961 article from Popular Science Magazine on the prevalence of odometer rollback fraud. (Page 59, if the link doesn't jump right to it)
Mechanical odometers could be tampered with in myriad ways. I have seen people literally use a screwdriver to manually move the numbers backwards, I have seen drills used and various other methods. Even now, you can have your 'mileage adjusted' digitally; it's a huge area of crime here in the UK and people are still getting jailed for it.
This link actually mentions Ferris Buellers Day off:
You can also see that mechanical odometers like this one are rewindable. When you run the car in reverse, the odometer actually can go backwards -- it's just a gear train. In the movie "Ferris Bueller's Day Off," in the scene where they have the car up on blocks with the wheels spinning in reverse -- that should've worked! In real life, the odometer would've turned back. Another trick is to hook the odometer's cable up to a drill and run it backwards to rewind the miles.
A point which no one has yet brought up is where the odometer cable is attached. If it is attached after the gearbox, then it will go forwards or backwards. If it is attached before the gearbox, then no matter whether you travel forwards or backwards, it will always move in a positive direction.
According to this article on madehow.com, speedometers attached to the back of the transmission started to be used from 1921 (prior to this they were attached to one of the wheel axles, which would allow for reversal of the mechanism)
So Hairy's point that mechanical odometers are automatically susceptible to reversal is not the case. I can't find any definite evidence for the percentage split between wheel attachments and engine attachments, though, but as @Oddthinking pointed out, it has been made moot anyway with the introduction of digital odometers.