You are probably using an older version of MySQL which has different password mechanism. You can fix the problem by simply updating to the latest version of MySQL. I used to have the problem too, but after I updated MySQL, it all works fine.
Thanks for the suggestion. I checked that, and its not it.
I loaded RadRails, and the data-browser worked fine. However, the WEBrick apps yet again would not even try to connect to the DB server; not failed password issues or whatever. Those I would see in the MySQL server log. No connection attempt at all. I am so far rather disappointed with my Ruby on Rail experience... not being able to even follow along in the tutorial is rather disheartening.
I wiped my Ruby and Rails environments twice and reinstalled to make sure I hadn't done something daft, but that didn't help. This morning I wiped Ruby & Rails again, and installed "Instant Rails" to see if I can get any further down that road. If not, I suppose the next thing to do is just set up a testing environment on my production Apache box to see if a deployed application works there at all.
As a I say, rather disheartening.