Find out a window's application

If you have a window on your desktop and you want to know which application it belongs to, open a console and enter the command

xprop

and click on the window you are interested in. You will get an output like

[...]
WM_CLIENT_LEADER(WINDOW): window id # 0x3200001
_NET_WM_PID(CARDINAL) = 7661
WM_LOCALE_NAME(STRING) = "en_US.UTF-8"
WM_CLIENT_MACHINE(STRING) = "tweedleburg"
WM_NORMAL_HINTS(WM_SIZE_HINTS):
                program specified minimum size: 0 by 0
                window gravity: NorthWest
WM_PROTOCOLS(ATOM): protocols  WM_DELETE_WINDOW, WM_TAKE_FOCUS, _NET_WM_PING, _NET_WM_SYNC_REQUEST
WM_CLASS(STRING) = "Navigator", "Firefox"
[...]

From this you can tell that the application identifies itself as "Navigator", "Firefox". If this is too unsure for you, have a look at the process ID PID, which is 7661 in the above example:

ps -A |grep 7661
 7661 ?        01:00:53 firefox-bin

By this you see that the process that manages the Window is number 7661 and called firefox-bin.