There are five federal service academies. 
They are:

U.S. Naval Academy located at Annapolis, MD

U.S. Military Academy located at West Point, NY

U.S. Air Force Academy located at Colorado Springs, CO

U.S. Coast Guard Academy located at New London, CT

U.S. Merchant Marine Academy located at Kings Point, NY

The U.S. Naval Academy, the U.S. Military Academy and the U.S. Air Force Academy are all Department of Defense service academies and have about 4,000 midshipmen and cadets attending each.  The U.S. Coast Guard Academy is a Department of Homeland Security service academy and the U.S. Merchant Marine Academy is a Department of Transportation service academy.  Both of these schools have about 1,000 midshipmen attending each.

All of these schools annually rank among the top engineering schools in the country.  Below are brief descriptions of each academy, provided by them, and a link to their respective web sites.

U.S. Naval Academy

U.S. Naval Academy

"To develop midshipmen morally, mentally and physically, and to imbue them with the highest ideals of duty, honor and loyalty in order to provide graduates who are dedicated to a career of naval service and have potential for future development in mind and character to assume the highest responsibilities of command, citizenship and government."

U.S. Military Academy

U.S. Military Academy

"To educate, train and inspire the Corps of Cadets so that each graduate is a commissioned leader of character committed to the values of Duty, Honor, Country:  professional growth throughout a career as an officer in the United States Army; and a lifetime of selfless service to the nation."

U.S. Air Force Academy

U.S. Air Force Academy

"To inspire and develop outstanding young men and women to become Air Force officers with knowledge, character and discipline: motivated to lead the world's greatest aerospace force in service to the nation."

U.S. Merchant Marine Academy

U.S. Merchant Marine Academy

"To educate and graduate officers and leaders of honor and integrity who are dedicated to serving the economic and defense interests of the United States in our Armed Forces and Merchant Marine, and who will contribute to an intermodal transportation system that effectively ties America together."
 

U.S. Coast Guard Academy
 

U.S. Coast Guard Academy

"The United States Coast Guard Academy is committed to strengthening the nation's future by educating, training and developing leaders of character who are ethically, intellectually, professionally and physically prepared to serve their country and humanity, and who are strong in their resolve to build on the long military and maritime heritage and proud accomplishments of the United States Coast Guard."