Say you are using Google Mail on your iPhone, everything is working perfectly, until one day it just refuses to connect to the mail server, with a message “The user name or password for Gmail is incorrect.”
This has happened to me a couple of times already, and it drove me absolutely nuts, since I could access Gmail through Safari, rechecked password in mail settings, even tried deleting an account and adding it again on iPhone, but nothing worked.
After also trying numerous other things suggested on various forums, the only solution that worked every time was to go to https://www.google.com/accounts/UnlockCaptcha?, enter your details and click on “Unlock”. Not sure why Google seems to lock access every now and then, but this resolves the issue.