Although there are many stories about Vashishth Jee, but here I will tell you only those stories where he had changed the course of Destiny of the people. Vashishth Jee was 1 of he 10 Maanas Putra of Brahmaa Jee in the beginning of the Creation.
(1) Vaivaswat Manu
The 7th Manu, Vaivaswat Manu, had no son in the beginning. Then Vashishth Jee performed a Yagya for him to get a son, but his wife Shraddhaa wanted a daughter, so at the end of the Yagya she requested for a girl. The priest offered the Aahuti and Shraddhaa had a daughter named Ilaa. Manu performed this Yagya for a son, so he was not happy. Then Vashishth Jee changed her gender and made her a male, named Sudyumn.
Vishwaamitra was a king, the son of King Gaadhi. Once he saw the glory of Nandinee cow and bent upon that the powers of a Brahmarshi had more powers than a king. So he left his kingdom and started doing penance to become a Brahmarshi. Now it depended on Vashishth Jee when he declares him a Brahmarshi. But his ego was not going and that is why Vashishth Jee was not declaring him Brahmarshi. After the penance of several thousand of years Vashishth Jee declared him the Brahmarshi and change his Varn from Kshatriya to Braahman. This is the only case of changing Varn in the whole history.
(3) Raajaa Dileep
It is believed that when Raajaa Dileep was getting married to Sudakshhinaa, the ends of the garments of the groom and the bride were tied very tightly. When Vashishth Jee inquired the reason of this tight knot, he was told that the couple would die the moment their knot was untied. Vashishth Jee then altered the course of their Destiny and averted their death.
(4) Raajaa Dasharath
Raajaa Dasharath of Soorya Vansh had no son in the beginning. He waited for many thousand years for a son. Vashishth Jee then suggested him to invite Rishyashring Muni to perform a Putreshti Yagya for him. Rishyashring Muni was the son-in-law of Raajaa Rompaad. Rompaad had married his daughter Shaantaa to him. And Shaantaa was in fact Raajaa Dasharath's daughter. Romapaad was his very good friend, and he had no child of his own, so Raajaa Dasharath gave his daughter to him. That is how indirectly Rishyashring was Dasharath's own son-in-law too. He came and he performed the Yagya then only Dasharath had 4 sons at the age of 60,000 years. Everybody knows that he did not live long after getting his sons, maybe at the most 30 years only.
(5) Changed of the Sequence of the Yug
I read this incident in Gita Press Tulasee's Maans Notes. I do not know how far it is true, but when it is given in Gita Press' Maanas Notes, it should be true, but I myself have never read it anywhere. Vashhishth Jee is a 1 of the 10 Maanas Putra of Brahmaa Jee. So Brahmaa Jee appointed him the family priest of Soorya Vansh. Vashishth Jee was not willing to accept this position as it was not a very respectable position for a Maharshi like him, but Brahmaa Jee persuaded him saying that "the Lord Himself will incarnate in this family in Tretaa Yug, you will benefited with HIs Darshan.".
Now original sequence of the Yug was Sat Yug, Dwaapar Yug (literally the second Yug), Tretaa Yug (literally the third Yug) and in the last Kali Yug. But Vashishth Jee could not wait for Tretaa Yug (the third Yug) to come as the third Yug, so he changed their order of their sequence. It was under his dispensation that after Sat Yug came Tretaa Yug and then came Dwaapar Yug.
That is how he not only changed the course of people's fate, but also even the sequence of Yug also.