The most established and proven form of collaborative editing.
Wikis usually don’t allow instantaneous updates, so editing by more than one person at one time can cause edit conflicts.
MediaWiki is the most established and proven wiki software, being used to run all the Wikimedia sites (Wikipedia, Wikiversity, Wiktionary…) many other major wikis, and all the notable green wikis.
The problems with simultaneous editing are greatly reduced in MediaWiki by section editing (allowing separate sections to be edited by different people at the same time) and a conflict edit warning with diff display.
EtherPad is open source software that can be installed on a web server to allow real-time collaboration, with multiple people adding to a single document, requiring simply editing a name before contributing.
E.g. http://etherpad.openstewardship.net is used for several documents related to the Coalition of the Willing.
It can have problems on a very slow connection, but generally warns quickly when connection is lost, preventing too much text from being input and lost.
Wave, Google’s open source tool. No longer being actively developed. Was hoped to be a replacement for email, but has had little uptake.
Has some few enthusiastic followers, but many who try it don’t understand what is so significant compared to other platforms (e.g. email or EtherPad, depending on the purpose).
Can be very problematic on very slow connections (e.g. where browsing speed rarely rises above 30-40 kb/s) – e.g. allowing entry of text, and indicating syncing, but failing to upload the text (and perhaps not allowing access to copy the text from the failed Wave page).
If thinking about using this for a collaborative project and hoping for wide participation, tread carefully – arguably you should consider alternative tools. Otherwise, at the very least make sure you provide or point to a concise guide for use of Wave.