Don't forget that all these things are actively monitored; the ILS installation includes a monitor that can see whether it is off-air (or lying), as does a VOR, a DME and so on. Since the first task in spoofing a Navaid would be to turn off the real one, any intervention would very quickly be detected. (As already mentioned, jamming a navaid to make it unusable would be easier, but that generally does not satisfy any terrorist objectives - it just makes the pilots job slightly harder).
The biggest threat (which there WAS a film about - an old B&W movie set in Ireland if I recall correctly) is spoofing ATC voice communications. If you can "steal" a frequency, and sound like you know what you are doing, you could radar vector traffic wherever you like...