Now 10 days into the Divvy experiment, I have some data. Since receiving my Divvy key on the 17th, I've taken 17 Divvy trips of between 6 and 46 minutes. (The 46 minutes included waiting 15 minutes at a station for a space to open up.)
A Divvy subscription costs $75 per year. The 17 trips I've taken just the past two weeks would have cost $38.25 on public transit. Or, since my average trip is around 14 minutes, it could be the equivalent of about $73-80 in cab fares.
Obviously, I've taken Divvy instead of walking a couple of times. And just as obviously, I wouldn't have taken cabs on most of those occasions as one can reasonably say that any weather appropriate for biking is also fine for waiting for a bus or train.
The biggest value, however, comes from my morning commute. On Divvy, it's 25 minutes door to door. On the LaSalle bus (the second-fastest way) it takes 45 minutes. That gives me 20 extra minutes in my day, which at my billing rate more than makes up for the annual fee.
Divvy is absolutely brilliant. I'm absolutely going to try the local equivalents next time I visit London or New York. Or other cities with similar systems: Montreal Bixi (the first in North America), Paris Velib' (the largest public bike share outside China), or someday Melbourne (helmet vending machines available as well).