Probably overkill, but you could use PHPList, which lets you send XML . From the site:
PHPlist can be set up to read a range of RSS sources and send the contents on a regular basis to users. The user can identify how often they want to receive the feeds.
You could also add some code to your home page template, where you would check if the day’s date is Monday (or whatever), then build a message with only titles (check the templates docs). You would also need a mechanism to make sure this only happens once or else it’ll be sent as many times as someone visits your home page!
Or, if you have access to crontabs, setup a cron event.
