Those MR-16 halogen bulbs can indeed be replaced by LED versions. The cheap ones cost $10-15. Tolerables ones are $30. Beautiful ones that are absolutely indistinguishable from halogen are, sadly, $70/ea. I expect this to change rapidly over the next few years.

Also, current MR-16 LED bulbs require that the 12V transformer be of the "magnetic" type, producing nice pretty sine waves of power, but they're more expensive. "Electronic" transformers generate choppy, ugly power, which is completely irrelevant to a classical light bulb filament but just doesn't work at all for LEDs.

(Fancier LED fixtures can work with just about anything, but there's nothing like that, yet, in the MR-16 form factor.)