When Galadriel was engaging in her gift giving to the Fellowship of Nine, she asked Gimli what gift he would have. In words that charmed her, Gimli said none initially, and when pressed again, he admitted he desired a single strand of her hair. She gave him three strands. What is interesting to note is that, thousands of years earlier, when the Noldor (the race of elves Galadriel and Elrond came from) lived in Valinor, Feanor Galadriel’s uncle asked her for a strand of her hair, and she, disliking him, refused.
It is said that Galadriel’s hair was the most beautiful head of hair in first Valinor, and then subsequently in Middle Earth.
Feanor later led a rebellion against the Valar, and left Valinor under a ban never to return. In some places it is said that Galadriel joined this rebellion, but mostly because she sought to oppose Feanor as much as possible. However, elsewhere it is said that she left Valinor on her own, and never participated in Feanor’s rebellion.
I just find it interesting that she refused her kin and gave to the Dwarf.