As you probably know, the Unity notification area (systray) whitelist is no longer available in Ubuntu 13.04 so you can't whitelist applications to be able to use the systray. If you can't live without an application that still uses the old notification area, here's how to get the Unity systray whitelist back in Ubuntu 13.04 (Raring Ringtail). Update: the PPA is now also available for Ubuntu 13.10.
Java and Wine applications have been hard-coded and continue to show up in the notification area but there are still some applications that don't have an AppIndicator and thus, can't use the systray. Some of the popular apps that can't use the systray anymore in Ubuntu 13.04 include: Truecrypt, Cryptkeeper, Blueproximity, Pidgin (if you don't want to use the Messaging Menu) and KeePassX (although KeePassX from the Ubuntu 13.04 repositories has the systray disabled in its settings and it can be enabled so for it you'll have to either use a PPA or build it from source).
How to re-enable the systray whitelist in Ubuntu 13.04 or 13.10
If you use such an application and want the systray whitelist back in Ubuntu 13.04 or 13.10, you can use a PPA that comes with Unity patched to re-enable the systray whitelist. To do this, open a terminal and run the following commands:
sudo add-apt-repository ppa:timekiller/unity-systrayfix sudo apt-get update sudo apt-get upgrade
Then, restart Unity by pressing ALT + F2 and entering "unity" or by logging out. Then open Dconf Editor, navigate to com > canonical > unity > panel and the "systray-whitelist" should be displayed there so you can enable some apps to be able to use the systray.
If you don't already know how to whitelist applications to use the systray, see: How To Re-Enable The Ubuntu Notification Area (Systray).
After adding an application to the systray whitelist, remember to restart Unity or else it won't work.