Bilbo Baggins
Legolas met Bilbo as he emerged from Thuranduil's tent in the dead of night, fresh from his negotiations with the Arkenstone. He stared at this strange creature, barely the height of a child, dressed in an elf-prince's armor and smoking a pipe. Mithrandir greeted him by name and sent him off again. From Mithrandir Legolas learned of the halfling, and that it was doubtless he who had freed the dwarves from his father's inescapable dungeons.
Legolas met the odd creature again after the Battle of Five Armies had concluded and Thorin Oakenshield been buried in state. Strange was this halfling, who had come so close to great wealth and yet had so little desire for it. Yet he was talkative about his adventures, at least, and Legolas found himself both amused and impressed by the small man's tales. Despite his stature, he had done deeds that warriors many times his height would never have succeeded at.
Legolas met Bilbo once more, sixty years later, as the aged hobbit returned to the Mirkwood and the Lonely Mountain to greet his friends and relive his adventures. His hair was white and his face lined, but he spoke with his usual cheer and wit. And it was from him that Legolas first heard the name Frodo—though he would not meet that Halfing for some years yet.
A/N: Bilbo is technically not part of the Fellowship, but he's so closely connected to the story that it's impossible not to have him. And while Legolas isn't mentioned in The Hobbit, it'd make sense for him to be at the Battle of the Five Armies, as well as on the journey back to Mirkwood.