DNS not resolving on Mac OS X
It turns out the solution was to bounce mDNSResponder:

sudo launchctl unload -w /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist
sudo launchctl load -w /System/Library/LaunchDaemons/com.apple.mDNSResponder.plist


This was obtained by a different coworker from this Server Fault question.

OS X 10.10.0 – 10.10.3, Yosemite

Apparently, mDNSResponder doesn't exist in Yosemite (OS X 10.10). You can restart descoveryd instead to fix these issues.

sudo launchctl unload -w /System/Library/LaunchDaemons/com.apple.discoveryd.plist
sudo launchctl load -w /System/Library/LaunchDaemons/com.apple.discoveryd.plist


OS X 10.10.4+, Yosemite

In OSX 10.10.4 the mDNSResponder has been reintroduced. So use the first one will work again.