I must admit I've never really got wikis until recently. Anything you could do with a wiki you could do with html and web pages, after all markup is markup and neither really imposes structure.
I've always thought in terms of connections and lists and related facts - not very visual I'm afraid and I've recently started using wikis as dot pointed lists (see here for an example on the tudor ascendancy and here for one on early medieval travel) as away of organising facts and links, any one of which could be expanded out to some text as seen is this slightly more complex example.
Using a wiki this way allows you to build a more complex living document piece by piece.
Next question - ignoring its inherent funkiness, what does google wave bring to the piece that a shared wiki doesn't?