Wikispaces is a hosted wiki, meaning that there's no software to download, maintenance is negligible, and administration is simplified. Your organization can have a wiki up and running in minutes, which can be a real benefit to those without a dedicated technical resource.
The flipside of that convenience is that, because it lives on the Wikispaces servers, power users may find that it's less flexible and extensible than a more complex, robust solution such as MediaWiki. It's also, by default, intended to be public-facing site, which may be an issue for teams that need to keep information confidential. A private wiki is available at an additional cost.
Like Wikispaces, PBWiki is a hosted wiki, and it claims that it makes setting up a wiki as easy as making a peanut butter sandwich. It's pretty darn close.
One fairly significant difference from Wikispaces is that a PBWiki site may be made private, via a password, in the free version. That's a nice feature for organizations looking to kick the tires without incurring any expense.
The sweet spot for DokuWiki is a small organization that wants to host its own wiki, but may not need the breadth of features (and associated complexity) of MediaWiki. DokuWiki stores its pages in text files, so there's no database administration, and its goal is to be fast and easy to use, which it accomplishes.
It's a good solution for creating and managing documentation and tracking changes over time. Plus, lots of plug-in modules have been developed for functions ranging from spec hecking to search enhancements. All and all, DokuWiki is a good compromise -- it doesn't seem to aspire to be everything to everyone. Instead, it's a heck of a tool for managing information and documentation for a small to medium organization.
TWiki is a structured wiki, which is a combination of a traditional freeform wiki and a more structured database. Because content can be added to the system using simple form-based applications, the data is structured so that it's better organized and should be easier to search for and find. TWiki also focuses on providing very granular control over access groups, meaning that it's easier to limit who can create, edit, or even read certain content. This may result in additional administration, of course, but this granular control is welcomed in situations where some information might be sensitive.
TWiki is implemented in Perl and no database is needed, as all data is stored in text files. This will probably appeal to less-technical administrators.