Apparently Twitter only allows you to download the last 3,200 posts you have made. While I am substantially short of this number at present, I thought it might be useful to keep an archive of these posts myself so I always had access to them.
The CMS I am most used to these days is WordPress and I recently came across a plugin and theme from Ozh which allows you to make an archive of your Twitter which looks like the new Twitter. This azurecurve Twitter Archive is now available; it has been themed to look very like my Twitter page but has all the functionality of WordPress.