Since I proposed the question, I probably should take a crack at answering it as well. (It wasn't as rhetorical as it may have seemed.)
The question was: what is the second example of a successful wiki after Wikipedia? I think I now have an answer -- BarCamp.
BarCamp is both a process and a philosophy about gatherings. You could argue its long-term relevance and whether it will survive the fad stage, but what I am interested in just now, is their use of technology.
The BarCamp web site is an excellent example of the use of a wiki. It is active, it is well structured, it is a perfect fit for its purpose, and it is making use of a wiki's unique capabilities.
I used to use SeattleWireless as an example of a successful wiki. SeattleWireless is a good example of a website run on a wiki. But it is not necessarily a successful wiki, per se. There is almost nothing about the site that is unique to wiki and could not as easily be run on almost any other website creation software with a bulletin board.
BarCamp on the other hand is completely dependent on the wiki capability (and philosophy) to achieve its goals. The point of the site is to make it as easy as possible for anyone to declare, organize, and announce a BarCamp. All three are achieved using the wiki structure, linking, and open authoring. Want to start a BarCamp? Create a reference to it and edit the resulting page. This automatically advertises its existence and encourages others to participate through the wiki just as they will at the event itself. (The guiding philosophy of BarCamp, like wikis themselves, is that everyone is welcome and the only rule is that everyone participate.)
So I have my answer. Are there others? Possibly. What interests me now is: if these are two examples of success, what is it that makes them successful and how would that translate in the use of wikis within corporations?