Which story of early pious Muslims had the most impact on you?

I would say it had to be Abdullah Ibn al-Mubarak and his encounter with a young woman when her was on his way to perform a nafl (supererogatory) Hajj.

He was born during the reign of Umayyad caliph Hisham ibn Abd al-Malik. 'Abdullah ibn Mubarak was an early, pious Muslim known for his memory and zeal for knowledge, collected hadith (muhaddith) and was remembered for his asceticism. Whilst on his journey he entered Kufa he saw a young woman sitting at a garbage heap plucking a dead duck.

It occurred to him that it was carrion so he asked her if it had been sacrificed. She replied that it had not been. "Then why are you plucking it?" he asked bewildered. She replied, "So that my family and I can eat it."

He informed her that it was not permissible to consume since it had died on its own.

She said, "My brother and I have only one piece of clothing. We have no food except what we find thrown in the dumps. Carrion has become permissible for us to consume for a number of days now (due to severe poverty). Our father was a rich man but his wealth was taken from him oppressively and he was killed."

Abdullah Ibn al-Mubarak asked regarding her family's whereabouts and she informed him. So he hired a man to take him there and when he found the house, he released his riding animal and gave it to the household along with all the goods that were on it. He handed over almost all of the money he had to the young woman, the money that was the provision for his Hajj, keeping only what was sufficient for his journey back to his land, Marw. He gave his provisions away saying, "This is better for us than our Hajj this year."

When his companions returned from Hajj, they came to congratulate him on his Hajj too. He said, "I did not go this year..." One of them said, "Subhan Allah! Didn't I leave my possessions with you whilst we were at Mina and on our way to Arafat?" Another said, "Likewise, didn't you buy things for me?" He turned to them saying, "I do not know what you are saying. As for myself, I did not go on Hajj this year."

Later that night, he had a dream wherein a voice called out to him saying, "Rejoice O Abdullah! Allah accepted your act of charity and He sent an angel in your form to carry out the Hajj on your behalf." [Tartib al-Madarik by Qadi Iyad and Ibn Kathir]