I see TiddlyWiki as one of the options or steps in a range of needs:
1) A text file or word document: I need to write some stuff down for me.
2) Tiddlywiki on my desktop: when I need to write down a bunch of related stuff that changes a lot and the word document takes too long to load/becomes hard to manage.
3) Tiddlywiki on tiddlyspot (or own-hosted solution): when I need to write down a bunch of relates stuff that I change a lot and want to let a bunch of other people see. (very similar to hosted static web pages but easier to set-up).
4) multi-user Tiddlywiki (hosted): when a few trusted people need to keep a bunch of related stuff organized but it isn't worth the effort/cost of created a full-on wiki (or sharepoint).
5) traditional wiki (i.e. phpwiki): when a bunch of semi-trusted people need to maintain a lot of related information and share it either with each-other or a lot of people.
6) Sharepoint and other things: We want something like a massive shared networked desktop environment with databases, fill-in forms, file storage, information pages, private pages for a lot of users (yes at this stage Sharepoint sucks but I don't know of any other solution that actually does what Sharepoint does when fully utilized).