Open-source:

Ward Cunningham's Smallest Federated Wiki, http://wardcunningham.github.io/

Elog retro UI, mature and flexible, http://midas.psi.ch/elog/

Treesheets, http://strlen.com/treesheets/

Linux Tomboy, https://wiki.gnome.org/Apps/Tomboy

Non-OSS indie apps:

Windows semantic wiki, Firebase db & Python plugins, http://www.connectedtext.com/

iOS, Mac, Windows markdown wiki, http://www.notebooksapp.com/

Notelynx on Android, interesting UI but no interop: https://play.google.com/store/apps/details?id=com.astrodean....

Tools discussion:

http://www.outlinersoftware.com/search/index/wiki

http://drandus.wordpress.com/

http://pauljmiller.wordpress.com/

My personal wiki is powered by Org mode[1] and includes more than 2,000 documents. No other note-taking solution that I've evaluated comes close to meeting my requirements as well as Org mode does.

Before I switched to Org mode, I evaluated many of the note-taking solutions discussed at the OutlineSoftware.com forum[2]. If none of the recommendations here at HN meet your requirements, you should consider browsing that forum.

[1] http://orgmode.org/manual/

[2] http://www.outlinersoftware.com/topics/tlist

My personal favorite is DokuWiki - https://www.dokuwiki.org/

Flat files so very easy to make backups, it's got your standard wiki functionality (revision history and all that good stuff) and has a fair few community-made extenions too

Edit: To address another comment here - it also has search functionality

I use gitit [1], which is open-source [2]. As a programmer, I really like being able to browse (less), search (grep), and edit (vi) via the command line. For my personal wiki, I do not even run the web server, saving RAM, though I can easily start the server if/when desired. Since it is backed by git, it is also easy to clone the wiki for offline usage and sync when going back online.

[1] http://gitit.net/

[2] https://github.com/jgm/gitit

Have you looked at TiddlyWiki? You could throw it on dropbox or a usb drive. http://tiddlywiki.com/

I have not used a great deal of Wiki software. Is there some sort of standard file format they can output? So if you want to migrate from one wiki platform to another, is it generally possible?

Not a specific format as such but most use at least similar versions of markdown - grab the markdown source of the page and paste it into another engine, it should turn out similar for the most part. If the destination wiki has a wysiwyg editor you might get away with just copying the text as is and pasting it in. All depends on the software though, so no there isn't a specific wiki format that I know of

The issue you'll probably come across is things like categories or custom boxes (MediaWiki) moving to another site.

http://raneto.com is a well designed option that I think would suit your needs.

I'm in the same boat as OP, but with an extra requirement.

It should support tagging and searching in text to be of any use.