You may consider miniature mains Neons - I did at £8 each and have had no tube failures for 2 years now. No halogens, leds or transformers to change either. Excellent light, low power, no heat and instant start up. Don't buy from DIY store but from specialist lighting retailer.
I'm not up to date with recent developments but LEDs are DC devices and Transformers are AC machines...
This from Wikipedia...
The current/voltage characteristics of an LED is similar to other diodes, in that the current is dependent exponentially on the voltage. This means that a small change in voltage can lead to a large change in current.
If the maximum voltage rating is exceeded by a small amount the current rating may be exceeded by a large amount, potentially damaging or destroying the LED.
The typical solution is therefor to use constant current power supplies, or driving the LED at a voltage much below the maximum rating. Since most household power sources (batteries, mains) are not constant current sources, most LED fixtures must include a power converter.
As with all diodes, current flows easily from p-type to n-type material. However, no current flows and no light is produced if a small voltage is applied in the reverse direction. If the reverse voltage becomes large enough to exceed the breakdown voltage, a large current flows and the LED may be damaged.
Good luck...
Peccavi, July 2009