I wouldn't present a typical LED with 200mA, as it's rather more than many LEDs are rated to handle. Some of the smaller LEDs get unhappy with anything over 50mA.
Different LEDs need different voltages. For example, red LEDs will often work around the 1.8V mark. Blue and white LEDs usually require more - sometimes as high as 3V.
Luxeons are the special case, as they tend to want ~4V, and several hundred mA to over an amp, depending on the model.
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