Unfortunately, system indicators cannot be moved in Ubuntu so you can't move the session indicator, the DateTime indicator and so on. Application Indicators are not easy to move either because you can't simply drag to reorder them, but you can specify their order in the Ubuntu Indicator Applet by editing a configuration file. Read on!
1. To change Application Indicators position on the Unity panel, you must edit a file called "ordering-override.keyfile" which is located under /usr/share/indicator-application . Since editing this file will change the settings for all users, you can copy it to ~/.local/share/indicators/application/ordering-override.keyfile and make the changes for your user only:
mkdir -p ~/.local/share/indicators/application cp /usr/share/indicator-application/ordering-override.keyfile ~/.local/share/indicators/application/
2. Now open the file by running the following command in a terminal:
3. In this file you should see the existing rules for Application Indicators order on the panel. The first one is nm-applet and has a value of "1", meaning it will be the first Application Indicator to be displayed on the panel, from right to left.
Using this as an example, you can add your own Application Indicators and specify their position by entering their name and a number like "clipit=7" which will make the ClipIt Application Indicator to show up as the 7th indicator on the panel (from right to left), if the other 6 indicators exist.
Here's an example in which I've set "indicator-weather" to show up as the first Application Indicator and "indicator-sysmonitor" as the last one (like in the screenshot above):
[Ordering Index Overrides] indicator-weather=1 nm-applet=2 gnome-power-manager=3 ibus=4 gst-keyboard-xkb=5 gsd-keyboard-xkb=6 clipit=7 indicator-sysmonitor=8
4. Once you finish tweaking the Application Indicators order, save the file and log out (restarting Unity doesn't seem to work).
Note: I couldn't change the Dropbox Application Indicator position in the Indicator Applet because I don't know its name so if you get this to work, please let us know in the comments.
Update: for getting the Application Indicator ID, see Jiří Janoušek's comment below.
Info via AskUbuntu.