Beleg "followed no man", and "could not be restrained". Beleg and his friend Mablung were the only Elves of Doriath to fight with the Union of Maedhros in the Nirnaeth Arnoediad (Battle of Unnumbered Tears), as King Thingol would have nothing to do with the war. Together with Mablung he was one of the great captains of the Sindar
Galadriel by Alan Lee. Many of the elves were tried and found lacking about 10,000 years before LotR takes place. Some of them (including Galadriel's brothers) abandoned many of their own to die of cold and hunger; this was known as "The Kinslaying." This is why Galadriel seems surprised when she says she has "passed the test" in FOTR - she had some slight involvement in The Kinslaying, and wasn't sure that she was going to be allowed to return to Valinor.