Textarea-backup.js (localStorage) is based on Textarea Backup by broquaint. The main difference between them is data storage.
The script by broquaint is using GM_getValue/GM_setValue, proprietary Greasemonkey functions. As far as I know, only Firefox Greasemonkey support it.
Mine script using HTML5 localStorage. Last versions of Firefox, Chrome, Safari, Opera, and Internet Explorer support it.
Open twitter.com and type something in the status box. Close the tab. Open twitter.com again. Your text will be still there.
For Firefox Greasemonkey, Google Chrome, and Safari GreaseKit users: just click on textarea-backup.user.js
For Opera users: download textarea-backup.user.js and rename it to textarea-backup.js (without “user”).