There are numerous ways to archive tweets but rather than use yet another tool, I prefer using Google Reader to preserve the tweets I mark as favorite on Twitter. Google Reader can preserve your tweets, favorites or those of others from the time you subscribe to a corresponding Feed.
You can access any individual public users timeline or their favorites in RSS, ATOM, XML and JSON formats:
https://twitter.com/statuses/user_timeline/<username>.rss
https://twitter.com/favorites/<username>.rss
Replace the username in the links above with the Twitter handle.
To track your own timeline with updates from your follower, try this -
https://api.twitter.com/1/statuses/following_timeline.rss?user=<username>
To track your own timeline with updates from your follower, try this -
https://api.twitter.com/1/statuses/following_timeline.rss?user=<username>
With Google Reader's "Send to" feature, you can post links from a subscribed Twitter feed to other social networking sites like Facebook, Reddit, Delicious etc.
Also see: