Must I install Google Apps again after installing a new ROM?
If you don't install the Google Apps package the first time, you won't have access to anything that relies on Google's services framework. This means things like:


Google Play
Google Talk
Google Maps
The Gmail application


...etc, won't function on your device because they will lack the libraries needed to run.

You do not need to re-install the Google Apps package every time you update CyanogenMod. It will essentially back up your current ones and then re-install them during the flashing process. Simply flash the updated ROM however you normally would.