Nigel Spivey's scholarly book, "The Ancient Olympics," says that in addition to the stade, a dash that in Olympia was 192m around the stadium track (they had both covered and open air tracks in Greece), they would run diaulos, up and down the stadium around a hair-pin turn, and they would run up to 24 stadium lengths, which was close to 5,000 meters but more often about 12, which was 2,400 meters. The stade was inconsistent from stadium to stadium, going from 177m at Delphi to 210m at Peramon. No time was kept. They were all races against other competitors. There was great respect for the running champions. "Fleet-footed" Achilles was the hero/goat of the Iliad. Koroibos of Elis was the first recorded champion of the ancient Olympics for winning the stade. In the vases for champions, they are typically depicted as having the physique of sprinters. As for marathon, the battle of Marathon in 490 bc between Greeks and Persians saw Pheidippides (or Philippides) sent from Athens to Sparta 160 miles to get help or Eukles ran from Athens to Marathon to fight in the battle and then ran back, dying from the effort (all this from Spivey, 116-17). They also had a hoplitodroms, a sprint of 2 lengths of the stadium in armor and a shield (119). The fact that the Greeks held the Olympics for over 1100 years, that there was intensive training for full-time quasi-professional athletes trained at gyms throughout the Mediterranean but especially in Greece, with many of the best from Sparta, and that there were distance races of 2.1-2.4k as well as roughly 400m and 5000m shows that there were probably exceptionally good runners who would break 4 on a modern track.
There are also some documented ultra and mile feats among Native Americans in the 19th century. Peter Nabokov's "Indian Running" is a good source for many of the different kinds of running traditions in the Americas. He writes of road stretches of 2500 miles from n. Ecuador to southern Chile with runners like those in Rome, Persia, and China. A coastal stretch was 1100 miles. The job of many would be to carry messages and other things along parts of this route as fast as possible, where there would posts in the 15th century every 2 miles or so, and the chasqui would blast a conch shell trumpet and yell a message on ahead and hand over a quipu message and then the next runner would run two more miles hard to the next stone shelter (20). They worked 15 day shifts. Messages could be sent this way about 150 miles a day during the civil wars after the Spanish conquest (21). Runners could cover Lima to Cuzco in three days when it took the Spanish 12-13 days by horse. One Hopi messenger in N. America would take messages 72 miles out and 72 back with one runner in 36 hours with an answer, wrote George Wharton James in 1903. A Hopi left a pueblo at 4 p.m. and 8 hours later delivered a message 65 miles away by night and then ran back home. That is under 7 1/2 minutes per mile, so either reflected incredible ability or is exaggerated. Edward Curtis claims a Hopi carried a note and returned over 200 miles in 3 days. Another Hopi, Charlie Talawepi, was said to have run 156 miles in under 24 hours carrying a message to Flagstaff and back (in Tuba City?). (Nabokov, 22).