Feanor and Gimli...

[Boromir88]

I believe it's quite clear Galadriel didn't give Feanor her hair because Feanor wasn't lets say as "nice" or "pleasant" as Gimli. Galadriel saw that Feanor didn't want her hair like Gimli did. Gimli wanted it so he could cherish it and think of the lady. I don't know much about Feanor except he was full of pride and arrogance.

Someone earlier said it was to honor Gimli, I agree, Gimli was an honorable person to have in the fellowship. He was a good companion and even Aragorn was impressed of his skills with the axe. As I said earlier I believe Galadriel saw the compassion in Gimli and it was a gift he wanted to cherish and not want for a prize, as I believe Feanor did.

[Lalaith]

Bear in mind what Galadriel said when Gimli asked her:

For none have ever made to me a request so bold and yet so
courteous.

In other words, his request was as bold as Feanor's, but he asked more nicely...
But seriously, I think it was much more than that. The significance of the request was certainly not lost on those present:

The Elves stirred and murmured with astonishment, and Celeborn gazed
at the Dwarf in wonder,

Galadriel knows it is time to end the ages-long feud between elves and dwarves. Her kindness and understanding of Gimli, and his rather touching devotion to her, is the first proper elf-dwarf exchange of warm feeling, and helps facilitate the subsequent friendship with Legolas. By her actions, Galadriel has strenghtened the bonds of the Fellowship which she has seen is in danger of foundering - and thus helped in the defeat of Sauron.

[Lhunardawen]

I agree, Lalaith. By giving Gimli the three strands of her hair, she took the first step in the reconciliation of Elves and Dwarves. And none could have done it better, since both Gimli and Galadriel are respected and well-known in their races. Also, it was said that Galadriel had an intense hatred for Fëanor even before he asked for some of her hair.