Shantanu and Ganga
Once while strolling on the banks of the river Ganga, Shantanu saw a maiden of exceeding beauty. So enthralled was he by her charm, that he asked her to be his wife. She agreed, but put forth a condition, that at no stage shall the king question her actions, or she would leave him. He agreed to her condition and their marriage was solemnised.
In due course she bore him a child, but at its birth she flung the baby into the river Ganga and returned smiling to the king. Pained and bewildered as he was by her action, he did not question her, for fear of her leaving his side. This act, of drowning their babies continued for six more children.
When, at the birth of their eighth child, his wife left to throw the baby into the river, Shantanu, who had so far bore his children's fates with fortitude to honour his promise, could no longer suppress his anguish. He finally burst out and questioned her as to why she would perform such an act upon the birth of a child. Thus he broke his promise. The maiden revealed her identity. She was Ganga, the goddess of the river. As the king had gone back on his words, she would have to leave him. She told him that she would not kill this 8th child, but would take him with her, and present him to the king in due course.
Shantanu was saddened by her departure and waited many years for the return of his son. As promised, the goddess returned his son, now grown into a young lad. His name was Devavrata and would become famous by the name of Bhishma, a central character of the Mahābhārata.
Shantanu and Satyavati
When Bhishma had grown into a young handsome prince, Shantanu came across Satyavati, a ferryman's daughter, and fell in love with her. The ferryman agreed to the marriage on condition that any child Satyavati bore him would inherit the throne.
King Shantanu was unable to give his word on accession as it would be unfair to Bhishma, the rightful heir to the throne. However, Bhishma came to know of this and in a magnificent gesture of renunciation and sacrifice for the sake of his father, gave his word to the ferryman that he would renounce all claims to the throne, in favour of Satyavati's children. To reassure the sceptical ferryman further, he also vowed life-long celibacy to ensure that future generations borne of Satyavati are also not challenged by his offspring.
Shantanu and Satyavati went on to have two sons, Chitrangada and Vichitravirya. After Shantanu's death, Satyavati continued to rule the kingdom with her two sons, with help from Bhishma.