"Oh hello, if you only give me your username and password to google's services, and also your SSN, and CC number and PIN, and your birth date, name and address; I need it all but I won't misuse it, honest."
That's what I hear when someone asks me for my name and password, for an e-mail service no less: what do most password-recovery systems use? Oh, right, your e-mail. The access to which you've just shared with an anonymous stranger. On the Internet. But hey, Facebook also asks for the right to ruffle through your e-mails, and they wouldn't be evil, so no problem, right?
Also, your app now needs to store username+password, as it will essentially become the user, as far as Google is concerned. I trust Google not to leak my name and pass; OTOH I absolutely do not trust you not to leak those (either intentionally, or through an outside hack, or an inside disgruntled employee). I do remember a related question about a similar service logging in as you.
@Pekka is right, if you're trying to use the user's access to Google, you should do this using Google's OpenID endpoint, as it's explicitly made for that situation, yet doesn't give you the control over the user's account. (I'm assuming you are not trying to phish the username and password)