Just few days ago I started getting authentication errors when trying to synchronize my PDA (HTC Artemis) with Google account. It had been working without any problems for few week, then suddenly stopped. I was trying to remove the server from active sync and re-add it, reboot both pda and laptop but nothing helped. I tried to search the internet and despite there is a lost of posts in forums asking for the same or similar problem (some of those related to Google service being down, some of those to other stuff) there is no clear advice. Then I found out one post mentioning blocked captcha for google account and after few secs I was able to sync my phone with google again.
After that I realized what actually happened. Some day I was trying to install Gmail client in my PDA and could not log into my account through it. It was still displaying index page with fields for user and password, after entering correct values it displayed error message stating that I entered bad username/password. I have tried it again for few times as I was pretty sure that credentials I am entering are correct - and then the client started to show also captcha field as usual. In that moment I gave up and close the client. I would never thought that this could be the reason for sync errors through the Exchange server, but it was! So what to do for fixing this? The solution si pretty easy but as usual, almost unknown to anyone.
Got to Google Captcha Unlock page (you can use your computer for that, it doesn't need to be done through blocked PDA) , simply enter your username, password and captcha text. If everything is correct, the page display message that the account was unlocked and you can try to run sync.