[AoyW] TiddlyWiki, an Offline Browser App
TiddlyWiki's presentation concept is also unusual; it acts like a collection of blog entries which are displayed in an arbitrary order according to how you hit item links. Items are inserted into the page as you click, which is certainly preferable to popping up windows or loading whole new pages for small snippets of content.
TiddlyWiki delivers only part of the web experience to personal notetaking: hyperlinking within a single page. That's a feature now conspicuous by its absence from most desktop software. However, the notion of a web (interlinked pages, each with definite content) is absent from this "web app". If a wiki is an edit-in-place web, then TiddlyWiki is not a wiki at all, it's a structured text collection with a fixed schema and full-text (non-indexed) search.
Also missing from the standard web experience is any kind of multi-user access, since it's bound to a single browser. You can upload a TiddlyWiki HTML file to a web server to simply publish it, which is how their web site is built. Shared entries which propagate to a server or peers automatically would make this a much more interesting environment. Also useful would be a way to incorporate non-HTML content, e.g. a table of numbers clipped from a spreadsheet, or some SVG for a pie-chart.