After Suttleworth's bizarre decision to hard-code the whitelist for the systray, a developer created a patch to allow people to continue to use applications that use the systray with Ubuntu.
Unfortunately, the patch's creator is now too busy to maintain it. This means that since the latest updates earlier this month, the whitelist no longer works (again).
Canonical's "solution" was to instruct us to raise a bug report for each application that doesn't work, but of course those bug reports have been ignored.
So…
How can I re-enable the systray? Its absence is creating difficulties for me.
I am using Ubuntu 14.04 64-bit.
Answering the question by @GGleb
Command
gsettings list-recursively net.launchpad.indicator.systemtray
Results
net.launchpad.indicator.systemtray disable-indicator false
net.launchpad.indicator.systemtray started-the-first-time false
net.launchpad.indicator.systemtray static-x 0
net.launchpad.indicator.systemtray static-y 0
net.launchpad.indicator.systemtray tray-is-static false
I notice that tray-is-static toggles when I middle-click the icon.

