This is kinda bizarre so I'm posting it just to make the fix more googleable. I'm lying in bed this morning checking my email on iPhone and get this error:
I get the same error on all five gmail accounts. This sucks. I figure Gmail is down, but I can sign in using the web browser. I go to my workstation -- let me point out that this means actually getting out of bed while it's still dark -- and my Mac Mail app can't download gmail either.
It takes a while and a few visits to different websites, but I do find the answer here at MadeByMark.com. I'm posting it here just to make the answer easier to find in case you get hit by the same strangeness.
Gmail apparently locks your account for some unknown reason and you have to go to one of their pages (https://www.google.com/accounts/DisplayUnlockCaptcha) and unlock it.
Indeed, this immediately unlocked the accounts. There are better ways to start the day, but mornings are always pretty, and I had some decent coffee to grind.
H. Doug Matsuoka
11 November 2010