Above bumper/tire height and it's time to be cautious, and anything up to the tops of the wheel openings is asking for it. The best thing to do is to enter the water and maintain a slow speed such that you get a "bow wave" out ahead of the bumper/hood instead of the water crowning against it.
Of course, with water up to the top of the tires or so, you'll likely get water in the doors anyway.

Brent