Note that MR16 only describes the bulb shape. There are MR16 bulbs in various voltages so first you need to make sure you are using the right bulb.

MR16's typically are operated at less than 120V (typically 12V) which means there will be a transformer somewhere. The transformer could either be integral to the fixture (usually a lump on the side) or located elsewhere. In the case of the latter, it's typically a black box with 120V wires on one side and two or more smaller wires coming out. It should be marked (though sometimes it's black on black etching on the plastic). Such a transformer can typically run mulitple fixtures.

If only one fixture is bad in a set I would likely suspect the fixture itself is bad. These things typically have a rather fragile base where the bulb plugs in. If after removing the bulb look up and see if you see cracking or burning on it. This is typically a sign the fixture is shot.