If you've had problems logging in, through the website or through an email client and you're positive you've got all the settings right AND you're positive you've typed and retyped AND retyped your username and password correcctly and it STILL doesn't work... here's something you should try.
Remember to close all other online and offline email activity related to the account in question first.
For Gmail users...
For Google Apps users...
Give it a few minutes and retry. It should be up and running.