Install the pywin32 extensions. Then you can do the following:
import win32com.client as comclt
wsh= comclt.Dispatch("WScript.Shell")
wsh.AppActivate("Notepad") # select another application
wsh.SendKeys("a") # send the keys you want
Search for documentation of the WScript.Shell object (I believe installed by default in all Windows XP installations). You can start here, perhaps.
EDIT: Sending F11
import win32com.client as comctl
wsh = comctl.Dispatch("WScript.Shell")
# Google Chrome window title
wsh.AppActivate("icanhazip.com")
wsh.SendKeys("{F11}")