Your company can make you double up on security with Google Apps "two-step verification." But even if it doesn't, you should do this on your own.
When turned on, it requires you to input a regular password, and a special one-time password sent as a text to your mobile phone. Every time you use a new computer it doesn't recognize, it sends a new one-time password. So bad guys can't get into your account on an unauthorized computer even if they learn your password.
You can set it up to refresh once a month, so it doesn't bug you too often.
From any Gmail, click on Settings (click the gear in the top right ) > Account > Click 2-Step Verification > Go through the step-by-step process.
Pro tip: download and use the Google Authenticator app which gives you other options besides a text message to get the second password and allows you to login even when your device is in airplane mode.