This Google Script will fetch and parse the XML RSS Feeds of any Stack Exchange website. You can then use the MailApp service to automatically push the content of the RSS feed to another email address on a regular basis. Or you can build an RSS to email service using Google Scripts.

function parseXML() {
  var feed = 'http://stackexchange.com/feeds';

  var xml = UrlFetchApp.fetch(feed).getContentText();
  var root = XmlService.parse(xml).getRootElement();
  var atom = XmlService.getNamespace('http://www.w3.org/2005/Atom');

  var entries = root.getChildren('entry', atom);

  for (var i = 0; i < entries.length; i++) {
    var title = entries[i].getChild('title', atom).getText();
    var categoryElements = entries[i].getChildren('category', atom);

    var updated = entries[i].getChild('updated', atom).getValue();
    var url = entries[i].getChild('id', atom).getValue();
    var summary = entries[i].getChild('summary', atom).getText();
    var user = entries[i].getChildren('author', atom)[0].getChild('name', atom).getValue();
    var userURL = entries[i].getChildren('author', atom)[0].getChild('uri', atom).getValue();

    var regexSubSite = /http:\/\/(.*?).stackexchange\.com/.exec(url);
    var site, siteURL;

    if (!regexSubSite) {
      // If it's not a "subsite"...
      site = /http:\/\/(.*)\.com/.exec(url);
      site = site ? site[1] : 'noneFound';
      siteURL = site ? 'http://www.' + site + '.com' : 'noneFound';
    } else {
      site = regexSubSite[1];
      siteURL = regexSubSite[0];
    }

    // url     - Question URL
    // title   - Question Title
    // user    - Question Author
    // userURL - Author Profile URL
    // site    - Stack Exchange Site Name
    // siteURL - SE Site URL
  }
}