Best hosted wiki solution for private wikis?
I previously asked about <a href="http://stackoverflow.com/questions/22117/how-do-you-organize-your-online-resources-and-researched-data">how people organize their online resources and researched data</a>, where one of the suggested tools was using a private wiki. 

I want to try this out and thus I am looking for a hosted wiki where I can store my thoughts, ideas and project documentation.

My requirements are:

* Must be hosted by a third party.
* Must be free or cheap.
* Must allow private wikis.
* Must provide some way to back up my data, ideally with complete revision history.
* Should have a good wiki implementation which is easy to edit, easy to organize and  with adequate searching capabilities.
* Would be a bonus if the wiki implementation is a standard, so I can migrate my data to another site or a self-hosted version in the future.

It would also be useful if the host also provided public wikis (with access control) and mapping of my own domain name for the wiki. This is not a requirement for my private wikis, but if they provided it I might be able to use the same host for public wikis on my public or open source projects.

So, are there any sites out there that provide this?
Best hosted wiki solution for private wikis?
===

I previously asked about <a href="http://stackoverflow.com/questions/22117/how-do-you-organize-your-online-resources-and-researched-data">how people organize their online resources and researched data</a>, where one of the suggested tools was using a private wiki. 

I want to try this out and thus I am looking for a hosted wiki where I can store my thoughts, ideas and project documentation.

My requirements are:

* Must be hosted by a third party.
* Must be free or cheap.
* Must allow private wikis.
* Must provide some way to back up my data, ideally with complete revision history.
* Should have a good wiki implementation which is easy to edit, easy to organize and  with adequate searching capabilities.
* Would be a bonus if the wiki implementation is a standard, so I can migrate my data to another site or a self-hosted version in the future.

It would also be useful if the host also provided public wikis (with access control) and mapping of my own domain name for the wiki. This is not a requirement for my private wikis, but if they provided it I might be able to use the same host for public wikis on my public or open source projects.

So, are there any sites out there that provide this?