Signs point to….
And Jason points tantalizingly at their recently announced but as-yet unrevealed new product "Backpack." So is Backpack a wiki? It could be. I know 37Signal's lead developer, DHH, worked on Instiki. It's the kind of scope that would appeal to them. And it's somewhere that they could use their design talent to really improve the state of the art. Also, they talked for a while last year about a new product called "WriteBoard" that was never actually released.
Still, I don't think this is the answer. The "Backpack" name doesn't really work as a metaphor for a wiki. Writeboard was much better. Unless it were a purely personal wiki. Hmm. That's also the kind of thing that would appeal to 37Signals: Ignore huge sections of a market and focus in on one very narrow use case — but totally nail it.
In any case, it will be interesting to see who can come up with the best ten word formulation to explain a wiki — something I know to be a challenge when trying to promote wiki adoption.
UPDATE: One striking thing about reading the comments is how totally different ideas people have about what a wiki really is — driven mostly by how they use it. Is it an encyclopedia, a collaborative website, a personal online notebook, a journal, or a content management system? Wow.