Thanks for starting this great thread!
Here's my list:
1) His fighting spirit and "never say die" spirit. He consistently "fights above his weight" and never tanks a match.
2) His on-court enthusiasm, including the "vicht", the "lawnmower" and the bellows of "C'MOOOOON." While others think it's poor sportsmanship, I know that he's just completely "in the moment" and that's he reacting to being in a winning position, no offense to his opponent.
3) His lobs -- I love to hear the crowd go "awwwwww" when they kiss the line.
4) His work with Special Olympians -- Lleyton displays tremedous patience with them and continues his work, even though almost every sportswriter ignores his involvement.
5) His sense of patriotism and his commitment to Davis Cup.
Bonus favorite thing: His great cheekbones and cheeky smile