If your Webmail account should reach capacity, then messages sent to your account will be returned to the sender undeliverable. You will not lose any mail already stored in your account. Make sure to occasionally clear your old e-mail or save it to your local computer from time to time for archiving purposes.

When using a desk top based e-mail software (i.e. Outlook, Thunderbird, Eudura), and if you set your e-mail accounts to clear all messages off the mail server when retrieving, then the limits of e-mail stored on your local computer are determined by your desk top e-mail software settings.

Additionally, the Google mail server has such a large capacity (6800+ MB) that it is highly unlikely that you should run out of space.