Yes, there are plenty of options for the same. The most popular method is to use a mail client like Outlook/ Thunderbird. These applications store the emails in their local storages thus availing you back up. The only demerit it carries- the backed up emails might be missing the attachment and the contents.
Otherwise, you may try on Mail Backup X. This tool backs up emails automatically. Moreover, the Backup files are completely downloaded for offline access. To know more on how to backup Gmail emails, give this tool a free trial.