You need to enter a new code every 30 days or after deleting your web browser's cookies. On the sign in page click the option to "Remember verification for your computer" on your computer, and you won't have to re-enter your code for 30 days. Do not select this option for a public computer, such as a shared computer in an Internet cafe.
The verification code is used only to sign in to your Google Apps account and not any other of our company's applications.