1. Wikispaces
www.wikispaces.com

Wikispaces is a very large community of wikis and they offer free and paid accounts.  They have a special offer for teachers who are offered a pro account for free.  This means that the wiki can be protected and only users approved by the teacher can view the material.  This website does, however, require that all users be registered with them and that they provide a valid email address with the wiki.  This can be a limitation in the primary classroom.

2. Wikia
http://www.wikia.com/Wikia

Wikia is another free wiki provider that allows you to create a wiki with the option of making it available only to those members that the creator of the wiki chooses.  Wikia does not offer any special account types for educators and their free accounts contain advertising over which you have no control.  

3. PBWorks
http://pbworks.com

PBWorks provide individual teachers with a free wiki that they can use with one class.  The advantage of PBWorks over most other providers is that the students don't have to register to be able to use the service.  They have relatively cheap prices for hosting for more classes as well, and paying customers, as with all these providers, are given access to a host of extra features and support.