As you can probabably guess if you read my blog, I mostly use emacs
org-mode for my personal note taking and wiki needs. However, that
isn't alwasy the best way for a particular project and not everyone is
comfortable with emacs. At CCOM, we have a general mediawiki instance
for the whole group (70+ people) and a trac instance for coding
related wiki'ing, bugs, and svn/mercurial monitoring. At NASA, I've
been around a lot of twiki and elsewhere I've seen people using
MoinMoin. I didn't like twiki, but I saw Kanef do some amazing
whipped up. Monica was using Wiki On A Stick (WOAS), but version
0.12.0 has been super buggy. There is also TiddyWiki and commercial
software (what was it than J. Dingler used??).
Wikipedia: Comparison of notetaking software and Comparison of wiki software. Note: neither one has WOAS. There is Personal wiki, which is more the topic at hand.
So... what do people use and why? Things like Trac and such can be
backed up, but I can see cross machine deployments being trouble.