|Old notification area (before AppIndicators)|
The notification area (systray) was removed from the Unity panel with Ubuntu 11.04, but you could still use it by whitelisting applications which would allow the icons to show up in the notification area. But not any more!
A recent Unity update in Ubuntu 13.04 Raring Ringtail mentions that the "Notification area whitelist is obsolete", so you can no longer get notification area icons by whitelisting applications. However, when the notification area whitelist was introduced, there were many applications that didn't come with AppIndicators so it was a pretty big issue back then, but right now most applications that used to come with a tray icon now use AppIndicators, including popular apps like Dropbox, Steam, Skype (with "sni-qt") and so on.
Also, all Qt applications tray icons are automatically converted to AppIndicators thanks to the "sni-qt" package.
With the retirement of the notification area whitelist, Java and Wine apps have been hard-coded as the only software still able to use the notification area so this change only affects some old applications that don't come with AppIndicator support. But with the huge number of AppIndicators that exist today, you'll probably find similar or maybe even better alternative. For instance, you can find a huge list of applications that come with Ubuntu AppIndicators on AskUbuntu; we've also covered quite a few AppIndicators.
Click here for more Ubuntu 13.04 Raring Ringtail (currently under development) news.