You are constantly testing code just by compiling and using it. In some IDE you are getting sanity checks as you type. Unless you never actually run your code you are doing testing.

How much you test is really the root of this sort of question and the answer to that comes down to risk. You test as much as it makes sense to test from a risk management point of view. Testing everything or nothing is usually impossible. Testing next to nothing is usually a bad move. Everything in between is fair game depending on the risk level and exposure of your deliverable.