Legolas is a great example of Tolkien's love of characterization through type of being. Most (or even all) of his most important characteristics come from the sheer fact that he is an Elf. As an Elf, he can run on top of snow. As an Elf, he can hear the stones singing and can listen to the trees. And as an Elf, he uses a bow and arrow to fight off the Orcs of Moria. But beyond Legolas' Elf-ishness, he doesn't have a lot going on, at least not in The Fellowship of the Ring. Just wait until The Two Towers – that’s when you start getting a bit more Legolas-Gimli cross-cultural bonding. For now, Legolas is mainly present to give the Fellowship an Elf member.
Legolas' main moment of glory comes when the Fellowship (minus Gandalf) reaches Lothlórien. There, Legolas sides with the Lothlórien Elves against Gimli on the matter of a Dwarf needing a blindfold to go to the heart of Lothlórien. Luckily for Legolas and Gimli's future friendship, the whole Fellowship agrees to wear blindfolds. And then, of course, Gimli falls hard for Galadriel, so there are no hard feelings to interrupt future Dwarf-Elf bonding.
Finally, we’ll give credit to Legolas for one more thing. He is the son of King Thranduil of Northern Mirkwood. We actually get to meet Legolas’s dad in The Hobbit, when Bilbo steals from him (… long story. Check out our learning guide on The Hobbit for more on Bilbo’s unlikely career as a burglar). It's a nice piece of continuity that King Thranduil’s son is now part of the Ring Quest, along with Bilbo’s nephew and Thranduil’s old enemy Glóin’s son (Gimli). It’s like the Ring Quest is becoming a family business for these guys.