The Prophet (PBUH) said: "Everything with which a man amuses himself is vain except three (things): a man's training of his horse, his playing with his wife, and his shooting with his bow and arrow." - Sunan Abu Dawud 2513
Running is also Sunnah in Islam. Our Prophet (PBUH) said in this regard: "There is a gain for every step of anyone who runs between the two targets."
The Prophet (PBUH) said: "Practice archery and practice riding, and the you should practice archery is more beloved to me than that you should ride. All idle pastimes that Muslim man engages in are falsehood, except for his shooting of his bow, his training his horse, and his playing with his wife, for they are from truth." - Jami' at-Tirmidhi 1637
Umar ibn Al-Khattab (R.A.) wrote to Abu'Ubaidah bin al-Jarrah, saying. "Teach your children swimming and teach your fighters archery." - Musnad Ahmad 323
A Hadith by Ibn 'Abbas states that the Prophet Muhammad (PBUH) said: “Perform Umrah in the month of Ramadan, (as it is equivalent to Hajj or Hajj with me (in reward).”
Ali ibn Rukanah quoting his father said: "Rukanah wrestled with The Prophet (PBUH) and The Prophet (PBUH) threw him on the ground." - Sunan Abu Dawud 4078