It is most likely that patients will be uncomfortable about talking to their physicians mainly about issues that seem to them to be very personal. This will, however, vary from patient to patient and will depend on the strength of the relationship between the patient and the physician.
For example, it seems likely that there will be many people who do not feel comfortable discussing sexual issues with their doctors. Men might feel uncomfortable talking about impotence. Women might feel uncomfortable talking about issues of sexual desire or sexual response. This is because these are some of the most personal issues that a patient might have.
Patients might also feel uncomfortable talking about issues that they feel are shameful or embarrassing. These, too, can have to do with sex. A person might feel very uncomfortable if they feel that they have a sexually transmitted disease. They might feel uncomfortable talking about issues that might arise with functions involving body waste.
In short, people are most likely to be uncomfortable talking to their physician if they feel that their medical issue is in some way embarrassing or excessively personal.
In addition to pohnpei's response, the specialties of medicine that would be most likely to embarrass a person would by gynaecology, urology, andrology, oncology (if it were testicular cancer, breast cancer etc.) and some aspects of general practise. These are all because of the reasons pohnpei397 gave; these areas of medicine deal with the most private aspects of a person's life, and the areas of a person's body that are not disclosed to the public (and yet they are expected to show them to a complete stranger, that is their doctor or specialist).