Twitter has rolled out a service that lets you see and keep your entire tweet history. Go to your settings in Twitter, scroll to the bottom of the page and you will see a new section called "Your Twitter archive". Click the button and you'll be emailed your Tweet history.
The email will show you your Tweet history since joining Twitter, with a navigable month-by-month breakdown. It also allows you to retweet old tweets, just in case you think your followers failed to appreciate their full magnificence the first time round.
The feature is just for personal (as opposed to corporate) accounts on the micro-blogging site at present, and only for English-language users, although Twitter has said more variations will be rolled out "over the coming weeks and months".