I have a Kenmore dryer model number 110-66732500 and it seems the heating element has went out on it. I see this is fairly easy to replace but my dryer is only about 3 years old and is used for a single person household, therefore is used very rarely. Is it common for these elements to go out so quickly. Thanks

Heating element failures will fall into the following categories:

1. Too hot because of venting problems
2. Loose connections (From the panel to inside the dryer)
3. Atmospheric impurities (e.g. Damp location)

Further to K.I.S. reply : there is also the possibility of sudden equipment failure. A heater element can - specially when it gets too hot (K.I.T.'s overheating due to lint blockage) - just break down without any specific cause. Do not forget that a heater element is subject to great stress.
And although failure of electric material can normally be expected early in it's life and much later due to aging, it still is possible at any time in between. They call that the "bath tub curve". Starting with a sharp vertical peak at first use, than a long horizontal period of low failure, and than a slow curved line upwards due to fatigue.

All in all : you are just unlucky. Fortunately a heating element is not too expensive.

:)