I know that we can get hydrophobic amino acids, but are there any proteins in the body whose surface is hydrophobic? If so what is their typical function and where can they typically be found and if not why not?
Are there any proteins in the body whose surface is hydrophobic?
Sure. Although you are right in thinking that most proteins have hydrophilic surfaces, some are very hydrophobic. My favorite example is Elastin, it is the main component of the skin which grants it elasticity. In fact, the hydrophobic nature of elastin is what confers it its function. The idea, briefly said, is that a insoluble/hydrophobic structure will tend to minimize it's surface area with water, so if you stretch such a substance (i.e. increase the surface area), it will pull back to the minimum surface area state.
Reference: Li, Daggett. Molecular basis for the extensibility of elastin. Journal of Muscle Research & Cell Motility (2002).