They may have, I admit, but I can't think of any. The point is raising the standard Google Reader/Google Buzz/etc. free examples isn't really apropos.
As far as I know, never. I've been compiling a list of live and shut down services/products/etc (~299 so far), and while payment doesn't seem to be an important factor (plenty of shut down paid things, including many more advertising services than I expected), I cannot name a service which was under heavy development and was shut down during said development. However, I think that is just because development tends to stop before the final death knell. Reader, for example, used to regularly update and improve during its heyday.
The idea is to try to predict future shut downs, but it's turned out to be a lot more work than I expected...
All serious development has slowed down to a crawl. New developments are mostly cosmetic. Bugs never get fixed. Microsoft, miles behind not so long ago is now streets ahead with Office 365, and Google has quite clearly stopped giving a crap.
Google has never shown any interest in the long term pursuit of any product or service that couldn't be sufficiently exploited for advertising, directly or indirectly (collecting data to sell to advertisers), paid or unpaid.
It doesn't mean those will not happen again.