A personal wiki is like a regular wiki but personal, only one person can edit it.
You’ll notice that you yourself are on a personal wiki.
There isn’t much to be said about this topic that hasn’t already been said.

Reshuffle note: I’ve gone ahead and looked at this, and realized it’s kinda bad.

• Nameless Rumia's Wiki
• Compendium of Personal Ignorance
• EKsK - Everything Killsushi Knows

• Everything Shii Knows - Run by Shii, arguably started the whole personal wiki craze. I include it only because of its importance.
• World2ch Historical Society (Archive) - Run by 0037, the only dead personal wiki I bothered to go through. Has info on the early days of 4chan and the days preceding 4chan. The archive is maintained by killsushi.
• Everything Anon Knows - Run by HumbleFool.

I was planning to use MediaWiki for this wiki, but it turned out to be an even bigger pain in the ass to install than I previously anticipated.
I don’t recommend MediaWiki for personal wikis. DokuWiki is the better option for a personal wiki, it’s what I’m using now.
If you don’t want other people to see your personal wiki, or you’d like to build it up first before “publishing.” Then I recommend WikidPad or DokuWiki on a stick.

There is a difference in tone and presentation between the various personal wikis I’ve looked through.
Currently, it looks to me like there are 2 main wikis that the rest are inspired from.
Shii and 0037. Where those derived from Shii tend to be more professional, have more sources and keep the tone formal-ish. Those derived from 0037 tend to have “cruder” language, they have less sources and overall they feel more blog-like.
This is entirely just an idea I’ve had and there’s basically very little evidence.