If your tried several times, then steam send to you one e-mail for each time that you tried to sign in, so you need to wait to the last key to log, since each new key, cuase the expire of the prior.

Note: One time, Steam delayed ONE DAY to send me the verification key.

And I helped flesh out the answer further, like a never ending family guy cutaway. :P

You have to be faster, after all it's a verification code. Do it again and only once, wait for the mail and look for it in your inbox or spam folders. How hard can it be? Usually I receive the verification code seconds later (I use Gmail).

You can get the login menu to send you another email.

Do you use Gmail? Sometimes when I have to verify my account those emails get sent to one of the other two Inboxes in Gmail, usually "Promotions." You could try checking there if it's taking awhile. Once I had them resend the email three or four times before I saw that they were in a different inbox.

Guys you are wrong, the problem is Steam side. Please try again later, it's a server problem.

UPDATE: I got another email, I tried the code and it worked.