My house has a 110V/220V electrical service. I have a motor that says its rated for 220V. Can I use it at my work shop that has a 3 phase 120/208V electrical service?

Yes. 208V is a standard three phase voltage. The 220V rating of the motor allows it to be used in both a 240V single phase system as well as 208V system. You will not have quite as much power as you would when you were using it at home which provided you with a 120V/240V service but will likely not notice the difference. By the way 208V will actually give you a measured voltage probably closer to 210V-215V.