Having been through this experiance twice, I've found out that insurance-wise, it's far better to HIT THE DEER.
Act of God, no deductable, car gets fixed.
Trying to get an insuance company to believe that you wrecked your car dodging a deer, good luck.
Truth be told, in most cases you won't have the time to make that choice, as the deer tend to do that for you.
In Ohio, where we kill more deer with cars than anything else, it's against the law to take road kill deer without the proper papers. They call it poaching.
Last year there were about a dozen deer hit just within the city limits of Columbus. Not all are hit by cars.
One was a 300lb 10 pointer that crashed into a friends home,nearly killing him before the cops got there and killed the deer. He spent a day and a half in the hospital. He's also 83. True story.