The key properties of these web apps is that you can do a "File->Save Page" in your browser to get a personal private wiki. Now lets have a brief tour of these applications to have a idea of the ircapabilities.
TiddlyWiki TiddyWiki is a MicroContent WikiWikiWeb made by Mr. Jeremi Ruston. By MicroContent we mean self-contained fragments of contents that are typically smaller than the whole page. These are also called as "Tiddlers". TiddlyWiki aggreagates these tiddler items into pages that are loaded in one gulp and progressively displayed as user clicks hyperlink to read them. It allows anyone to create personal self contained hyper text documents. All the content reside in a single html document, needs no server side stuffs, and can be updated from the browser itself. It is published under an open source lincense.
It is possible to change the look and feel of this web-apps by suitable change of CSS (Not an easy task for begginers), and several beautiful templates have come up like TiddlyKubrick, TiddlyRin, Blue Mist, GTDone Style, Tiddly Tag Style, Tiddly Sinister, ZeldMan Orage Style. People have tried to build-up several variations of it like MyWiki and IeWiki.
The third version of TiddlyWiki has got a rich set of features like Compatibility of most modern browsers, Generation of RSS Feed, Auto Save, Save Backup, Custo Style Sheets Keyboard Shortcuts, Rich Foratting, Embedded Images and Macros.
And no doubt, because of such rich feature set it has been used by many people for different purposes like homepages, blogs, community portals, and writing Fictions too. A big list of such usages of TiddlyWiki can be found out at http://www.tiddlywiki.com.
You can get your own copy of blank TiddlyWiki here.
GTDTiddlyWiki Getting Things Done is a simple and effective personal productivity methods by David Allen. GTD Tiddly Wiki is a GTD adaptation of Tiddly Wiki by Nathan Bowers. The purpose is to give user a single repositary for their GTD lists and support materials so that they can create/edit lists.