Has anyone ever created their own Wiki?

What I am basically looking for are the following capabilities;

1) Free (yes, I'm a tight-wad);
2) Private - I really only want to be able to own read/write access my content, with ability to allow others to view content by application only (unlikely);
3) Similar basic functionality to Wikipedia - search capability, hotlinking to other topics, et cetera; and,
4) WYSIWYG set up and editing.

Whether it is something that is easily set up locally or on the internet is just fine.

Anyone know of any good providers?