Freshet Backup makes a copy of your WordPress database on a schedule and keeps it in your Dropbox. Connect Dropbox once under Settings Freshet Backup and it takes care of the rest.

Set up in three steps. Press Connect Dropbox, press Allow, paste the code. No developer account or API keys needed.
Runs on a schedule. Every hour, every 6 hours, daily or weekly. Or press Run backup now.
Kept in your Dropbox. The newest seven backups are kept and older ones removed. A backup only counts once Dropbox confirms it arrived complete.
Tells you when something is wrong. If a backup fails or does not happen on time, a notice in wp-admin says so, with the likely reason and what to do.
Safe on copies of your site. A copy of the site on a staging or development server does not back up into your Dropbox.
Private on your server. A backup waits in a folder nobody can download until it is in Dropbox. If the plugin cannot confirm the folder is private, it makes no backup.
Off until you connect. Nothing runs before Dropbox is connected. Dropbox is the only outside service it uses; see External services below.

It backs up the database only, not files or uploads, and there is no restore button: the FAQ shows how to restore.

Part of the Freshet plugin suite. Full documentation: freshet.studio/docs.

External services

Freshet Backup uses one outside service: Dropbox, run by Dropbox, Inc., to store your backups. Nothing is sent before you connect Dropbox, and nothing is ever sent to Freshet Studio or anyone else. There is no tracking.

When you press Connect Dropbox: your browser opens Dropbox’s sign-in page (www.dropbox.com/oauth2/authorize), where you approve access. When you paste the code back, your site sends that one-time code, the app key and a single-use verifier to Dropbox (api.dropboxapi.com) and receives a token that lets it reach its own folder in your Dropbox.
On every backup: your site trades that token for a short-lived access token (api.dropboxapi.com), uploads the compressed database backup to its folder (content.dropboxapi.com), lists the files in that folder, and deletes its own older backups beyond the number it keeps. The backup holds everything in your site’s database tables.
When you press Disconnect: your site asks Dropbox to withdraw its token (api.dropboxapi.com).

If you set your own Dropbox app in wp-config.php, the same requests go to the same hosts with your app’s key and secret.

Dropbox terms of service and privacy policy.

Before each backup the plugin also requests one test file from your own site, to check that the backup folder cannot be downloaded. That request goes to your site’s own address, not to an outside service.