Juzt a small note:
It's free only for citizens of Tallinn, not for e.g. tourists.
I wonder if that was a rational decision. Is the cost of authenticating higher or lower than the revenue gained from tourists? If the revenue difference is actually that large, they probably could have just rolled it into the typical "hotel taxes" most places have.
The revenue gained is not from tourists but from people living in neighboring municipalities (but working in Tallinn) registering them as citizen of Tallinn and therefore bringing their tax money.
Impressive. Redstone Arsenal in Alabama only has 40K people or so. At least in the 90s when I was at the Ordnance school. Which has apparently moved to Ft Lee since then. The free buses were rather convenient.
Bangkok keeps on extending its free bus service, and its quite extensive.
Note that the bus system is essentially classed, since only the old, non-airconditioned, slow buses are free (and you can pay for better transit options).
Sydney, Australia does have a fee bus service that runs a certain route for key points. It certainly isn't all buses though. There are other cities in Australia that also do this.