I am transferring my domain to a new host but I have troubles backing up my email.

The procedure depends on the kind of Control Panel you are using. Simply locate the backup Link in your control panel's menu, and then proceed to download a full backup of your website. Usually, all your emails will be included in the backup file.

Thanks syskay, I actually thought of that but I needed clarification. Thanks again.

@skykay, you are correct about that. I will continue to from there. The backup will always include a copy of your emails if you are using cpanel. It will backup your site into an archive format [i think zip].
You can sometimes make use of the domain transfer resource which copies your site from your old to your new server including emails. This utility is usually in the whm cpanel [the reseller package of whoever sold the site to you], you can request that your webhost help you to transfer your files and email to a new server.