Perhaps the most famous, and lasting, of all cargo aircraft is the DC-3. Originally designed as a passenger aircraft, thousands were purchased by the Army and Navy during World War II, converted to the cargo role with the addition of large doors behind the wings. These C-47 Dakota served in every theatre of war, and were also widely used by most allied forces. Many thousands were later released into the civilian market at the end of the war, resulting in the formation of many small air freight operations.
One of the most first major dedicated-cargo designs was the Me 323 Gigant, a huge design with front-mounted clamshell doors. The design was hampered by underpowered engines however, and was too expensive for its load to be considered a success. A more successful design was the Fairchild Aircraft C-123 Provider, who's genesis stretches back to the Chase Aircraft assault gliders from 1943. In 1949 a powered version was built, and soon an order followed for 300 C-123B's, with many more after that. The C-123 would introduce the now-classic cargo aircraft layout, with a tail boom bending upward to leave the area under the tail clear for trucks to drive up, and a loading ramp that folds up to close the rear of the plane over the cargo area. This was followed by the C-130 Hercules and a number of designs of the same general layout and increasing capability, culminating in huge designs like the C-5 Galaxy.
One interesting piece of history is that the famous Boeing 747 originally started as a pure-cargo competitor to the Lockheed C-5 design. Both were built specifically to carry two standard cargo containers stacked on top of each other, with two stacks side-by-side (making a box of four). Boeing was worried that in case of an accident the containers would fly out the front of the aircraft and kill the pilots, so the cockpit was moved to a bubble on top of the fuselage. After losing the contract to Lockheed, they re-purposed the plane as a passenger design, one of the most successful in the world. A number of pure-freighter versions with clamshell doors in the front, similar to the original design, were indeed built, but rising operational and fuel costs have largely elimintated cargo container shipping by air.