Ryuk is definitely the most obscure character in the Death Note series. Despite of not knowing much, he still has quite some depth to his personality and is my favorite character. He finds humans amusing and really enjoys devouring apples!
I found Ryuk to play a influential role on Light. Even though Ryuk boldly stated that he would be hanging around in the human world purely for amusement, his commentary stimulates Lights cat and mouse game with L. In the very beginning, right after Light was outplayed by L who faked his death and then confirmed about Lights location, we could see Ryuk laughing, and exclaiming the brilliance of L. Light considered himself "The God of the new World" as the Death Note gave him a sort of supernatural power. Being outplayed by a mortal with no supernatural ability was bad enough, but having a Death God acknowledge the mortal and laugh at the scenario made it far worse. If Ryuk hadn't been there, his ego wouldn't have been damaged as hard as it was.
I also found Ryuk, although he exclaimed to be on a neutral side - to be impartial. At the time Light was being followed by the FBI Agent, Ray, Ryuk was the one who gave Light the signal that they were being followed. There was absolutely no reason to do so, but Ryuk exclaimed "It was getting creepy that the FBI agent was following them".Clearly a Death God who can neither be seen or killed by humans is very unlikely to be scared or feel creepy by a person who's following it. Light played accordingly and won that round against L. Ryuk's pick of partiality of this round was also peculiar as he picked the round where he lent a helping to Light to cross his line of morality and become more towards a sociopath. Light, instead of following his rule, killed people who represent law and justice in the modern society. This was controversial to what he was suppose to do, which was only killing the unjust and guilty. After the mass murdering of the FBI agents, it's understood that Light will not only kill the guilty, but anyone who is in his way.
In my opinion, there is definitely a small similarity between the western cross roads demon and Ryuk. Like the crossroads demons we hear of in western literature, Ryuk tries to make a similar agreement to Light. He offers his Shinigami eye's in return for half of Light's life span. Although the dealing is the same sort, he mentions why he strikes the deal and what he will do with what he gets. Unlike most demonic figures portrayed in Western Literature, Ryuk is honest and true what he says. If he was evil or had cruel intentions, he could do much more harm with the amount of power he holds but he doesn't. Maybe this is the reason he's a Death God and not a Death Devil!