TweetBackup does exactly what its name implies: backs up your Twitter posts (a.k.a. tweets). It's a free and easy service, and it has the potential to prove very handy.
To sign up for TweetBackup, you just click a button to authorize access to your Twitter account. There's nothing to install on your PC, and you don't even have to supply your Twitter password. The only requirement is that you follow @tweetbackup, a pretty miniscule price to pay for a free backup service.
Once that's done, TweetBackup will quickly back up your Twitter profile--your tweets and the people you follow. It does this on a daily basis. Backups are limited to 3,200 tweets, but that's a Twitter limitation.
If you click on the Export tab, you'll see that you have the option of exporting the backup in four different formats: CSV, RSS, Text, and HTML. (The HTML and CSV formats come with the permanent URL for each tweet, a nice perk.) Any of these files can be searched using standard methods, which is often a much better option than trying to search your own Twitter page.
So, why bother backing up your tweets? Well, if you're clever and prolific, who knows: you might just turn your tweets into a book someday. It worked for that guy and his dad.
By the way, TweetBackup is a spin-off of Backupify, a service that backs up not only Twitter, but also your Facebook, Gmail, Google Docs, and other accounts. Good stuff.