How can I kill a specific X window

If you use wmctrl -lp the PIDs are in the third column.

For a given window ID you can use

kill $(wmctrl -lp | awk '/^WID/ {print $3}')

(replace WID with your window ID)

Besides listing the PID as described in other answers by Florian Diesch and Serg, you can use -ic option to close the window directly:

$ wmctrl -ic 0x02e00085

wmctrl actually has another flag -p for listing PID.

bash-4.3$ wmctrl -lp
0x0380000a  0 4410   eagle Desktop
0x04800006  0 4275   eagle XdndCollectionWindowImp
0x04800009  0 4275   eagle unity-launcher
0x0480000c  0 4275   eagle unity-panel
0x0480000f  0 4275   eagle unity-dash
0x04800010  0 4275   eagle Hud

Once you know this, it's a trivial exercise of extracting that window's PID and passing it to kill

wmctrl -lp | awk '/Window Title/{print $3}' | xargs kill