LED bulb still emits light when turned off
There are two possibilities the switch is inserted:
- Switch switching the voltage line.
- Switch switching the GND line.
simulate this circuit – Schematic created using CircuitLab
The capacitors shown in the circuit are the capacities the (more or less) long lines form to GND.
If the 2nd circuit is what you have the lamp always is connected to alternating voltage. In that case there is a possibility of some very low alternating current flowing via C10 to GND even if the switch is open.
You can find out if your configuration is the 2nd circuit by testing with a one-contact neon test light. It is the case if the test light lights up when touching one of the two connections in your lamp socket even if the switch is turned off.
I would guess that your off-low-high switch has an indicator light so you can find it in the dark, so the LED lamp ends up in series with the indicator when the switch is 'off'.
Edit: For the lamp to emit visible light, current must be leaking across the switch.
Possible reasons are:
Indicator light (ruled out by OP)
Capacitor or RC snubber across switch to avoid EMI when switch is flicked (not seen often in North America, but might be a possibility in Europe).
Dimmer circuit that has an internal snubber and is not switched off entirely
damage (arcing and tracking or moisture) to the switch. A mechanical switch by itself should not leak enough to light an LED.
It will not draw more current than it would with the halogen lamp, and all but the last cause are nothing to be concerned about.
I took a hint from a previous comment and flicked the plug 180 degrees on the wall outlet. The bulb doesn't emit light when in the "off" position anymore.
It seems that the lamp's circuit was interrupting the GND line, like illustrated in @Curd's answer.