LEDs can run for 10s of thousands of hours. Couldn't find any lifespan figures for automotive use (didn't dig very deep), but, according to The Intertubes, LED bulbs for home use will last about 50,000 hours. Due to vibration, high temperature, etc, I'll guess that car LEDs will last about 10,000-20,000 hours - it's probably longer. You can find a better answer by googling "LED lifespan" and digging a little deeper than I did. Maybe try "automotive LED lifespan".
Turning LEDs on and off doesn't have the dramatic effect on lifespan that it does with incandescent, fluorescent, and some other types of lighting. For most consumer applications, you can ignore it. Electrical spikes from the alternator/regulator system may have a larger effect than on/off cycles.
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