Contribution pages for a specific user: go to the user's contribution page and use the toolbox link labeled "Atom" to subscribe to this feed
RSS feeds
Changes to any Wikipedia article: https://en.wikipedia.org/w/index.php?title=ARTICLENAME&action=history&feed=rss, where ARTICLENAME is the article's name as it appears in your browser's address bar (i.e. with spaces replaced by underscores, etc.)
User contributions: http://en.wikipedia.org/w/api.php?action=feedcontributions&user=USERNAME, where USERNAME is the name of the user whose contributions should be included in the feed
Watchlist feed with token
You can set up an RSS or Atom feed of your watchlist that is accessible even when logged out:
Go to the "Token" section and click the "Manage tokens" button
On this "Reset tokens" page, copy and paste the randomly-generated value token value for the next step
Your watchlist RSS feed can be found at https://en.wikipedia.org/w/api.php?action=feedwatchlist&wlowner=USERNAME&wltoken=TOKEN, where USERNAME is your username without the User: prefix and TOKEN is the watchlist token you copied from your preferences. If you would prefer an Atom feed rather than an RSS one, add "&feedformat=atom" to the Link of your feed.
Similar to your watchlist preferences, the feed of your watchlist can be customized by adding different parameters to the link of your feed, see documentation on Mediawiki. e.g. &hours=72&wlexcludeuser=USERNAME to display the maximum length and to exclude your own changes.
XML exports
You can export the contents of a particular article or set of articles in XML format via the Special:Export page. This special page allows exporting the history of the page as well (up to 1000 revisions). Test out the full-history export on a page with a short history, to make sure you know what you are getting.