Packrati.us is a service that makes it easy for you to bookmark your favorite links that you share and that others share with you on Twitter. Packrati.us will bookmark any link that you share, any link in a Tweet that you favorite, or any link that is shared with you in an "@" reply. Packrati.us works with Delicious, Diigo, Instapaper, Pocket, Historius, and Pinboard (not to be confused with Pinterest). Once you've authorized Packrati.us to work with one of your bookmarking services, you're ready to start bookmarking while you Tweet. If you are a Four Square user, you can tell Packrati.us to ignore those links from your check-ins.
If This Then That has been featured here in the past. If This Then That is a service that helps you automate tasks between services. Thousands of people have created If This Then That recipes for automating tasks like saving links from your Tweets to your Evernote account. If you're a Diigo user, you might want to try this IFTTT recipe for saving Tweeted links to your Diigo account.