Internet wikis that need a server, but can be run locally
The degree of difficulty for installation varies -- most PHP installations require an Apache Web server, and some may require mySQL as well. Windows users check out XAMPP for an easy-to-use Apache/PHP/MySQL platform.
TiddlyWikiClassic -- The original. More mature, has more useful plugins, and requires an additional JSON file stored in the same folder of your tiddlywiki when using Chrome or IE.
TiddlyWiki5 -- TiddlyWiki rewritten from the ground up based on HTML5 standards in order to to be as future-proof as possible. Currently in beta, lacking many features of the original (using plugins)(3/4/2014).
Stand-alone personal wikis that don't require a server or a browser
MobileWikiServer? -- an iPhone based wiki for personal use, or serving pages in a WiFi network. Also usable over a local WiFi network. Backs up to iTunes store, and exports to other users and to its cross-platform desktop version. See http://www.mobilewikiserver.com