The United States Postal Service is not a monopoly. It is a federal agency and thus is not bound by anti-trust laws.
Furthermore, a plethora of alternatives are available, FedEx, Airborne and UPS spring to mind immediately. The USPS is, arguably, the best run department in the Federal system. The USPS is the only Federal agency to turn a profit.
Lately they have come under fire for frequently raising the price of postage, however, the price of postage had been virtually unchanged for decades.
Of further note, A recent study I saw on CNN last week stated that postal workers are statistically NOT more prone to violence than workers in other professions.
Update: I have received information correcting my statement about the USPS budget. My informant claims that they are deeply in debt and that is the reason for their recent rate increases. I will admit that my initial information was several years old, but I stand by my claim that they are one of the best run federal agencies.