You can choose a keep a copy of all emails you send (including replies and forwards) in any folder you want. Make sure the Place a copy in checkbox is checked, and choose your folder.
Additionally, any email you send from this particular email address can be Bcc'd (blind carbon copy) to one or more email addresses.
This can be very useful when you are part of a team who collaborates on a project, for example. From there on, every email you compose will have one or more Bcc entry for each of the email addresses specified.
In the Bcc these email addresses field, use a comma (,) to separate email addresses, not a semi-column (;)
The email account whose settings you are editing can also save draft emails and templates in a custom folder. The defaults are respectively Drafts and Templates, both in Local Folders.
Thunderbird can also give you a confirmation message when you save the email you are editing as draft. ("Your message has been saved to the folder [blank] under [blank]", [Drafts] and [Local Folders] by default).
To enable successful saving notification, simply click the Show confirmation dialog when messages are saved checkbox. The confirmation dialog itself contains a checkbox that lets you turn off these notifications.
Ctrl+SSaves current email in Drafts