Does Gmail ever ask for my username and password?

"No. We feel strongly about your privacy and security. For your protection, we do not send unsolicited mass messages asking for passwords or personal information. We don't need this information to assist Gmail users.

If you've received a message that asks for private information, like your password, or directs you to a site that resembles Gmail, please note that the message did not originate with Gmail.

This practice is commonly called "spoofing." Spammers spoof by sending a fake email and then setting up a website, in an attempt to collect sensitive personal information and/or gain access to your Gmail account."

Search for "spoof" in the help page for more details.