The manga or anime begins with Ryuk and the other death gods in the Shinigami Realm. Ryuk was bored with the lack of activity as all the death gods are relaxing. So he decides to obtain a second Death Note by tricking the Shinigami King, write the instructions in English and drop it into the human world. The plot begins when Light Yagami found the Death Note in the midst of his school.
5 days later, Ryuk had a conversation with Light. The simple reason he gives about why he dropped the Death Note into the human world is that because he is bored. He tells Light that since he was the one who found the notebook, it belongs to him. If he does not need it anymore, he can pass it to anyone else. But when it is the time for Light to die, Ryuk will write his name down. Light then explains to Ryuk that he wishes to cleanse the world of evil criminals, and becomes the God of the new world. But Ryuk told Light that if he were to do that, the only bad person left will be Light, himself. Light ignores his comment, saying that he is plain serious about what he is doing. Ryuk then comments about humans being interesting.
The events of the show only gets to keep the death god entertained for 6 years
At the end of the manga, Light was revealed as Kira after his plan to kill everyone present in the warehouse was foiled. He was then shot five times by Touta Matsuda when he attempts to write Near's name down. Light then asks for Ryuk to write his enemies' names down. The police open fire on the death god, to no effect. It turns out that Ryuk was actually writing Light's name down. During Light's pleading, Ryuk reminds Light about what he said earlier that he would be the one who kill him, and that humans who used the Death Note will neither go to Heaven, or Hell, before returning to the Shinigami Realm. Light disgracefully dies of a heart attack from Ryuk's Death Note while laying on the floor in front of the SPK police officers.
In the anime, Light does not talk to Ryuk, but manages to escape from the warehouse, due to Teru Mikami's suicide. Light ran as fast as he could, but could not for long as his wounds were severe. Ryuk, watching from a distance as Light hides in another warehouse, comments that Light had lost. He does not want to wait around long during Light's prison term, so he writes the latter's name down, just as he promised in the beginning. Light dies peacefully soon after.
In the 2017 movie adaptation (which is loosely based on the original works), Ryuk appears as the secondary antagonist and is portrayed by Willem Dafoe via motion capture. His role is a lot smaller than it was in the anime, manga and original live action adaptations, however, he is still a prominent figure within the film and appears as being a tad more evil than in previous adaptations.
Powers and Abilities
Immortality: As a Shinigami, Ryuk has a infinite lifespan and is unaffected by disease and poison as long as he uses a Death Note to kill humans in order to take their remaining lifespan. He also can't be killed or injured by firearms, knives, or other weapons.
Intangibility: Like all Shinigamis, Ryuk can pass through walls and matter, and can't be seen by human beings, except if they are in possession of a Death Note, or a fragment of it.
Shinigami's Eyes: Ryuk can see the real name and the remaining lifespan of a human simply by looking at them. He can also make a deal with a human being possessing a Death Note by giving him the same ability in exchange of half of the remaining lifespan of the human.
Flight: Ryuk possesses wings, which he uses to fly from one point to another.
Let's just say this: you will feel the fear and pain known only to humans who've used the notebook. And when it's your time to die, it will fall on me to write your name in my Death Note. Be warned any human who's used a Death Note can neither go to Heaven nor Hell for eternity. That's all.
~ Ryuk to Light about the consequences of using a Death Note.
The human world is a boring place with boring people doing boring things.
~ Ryuk about the human world.
I don’t care if it is fortunate or unfortunate that Light picked up the Death Note. However… It is generally bad luck for a person to be followed by a God of Death.
All humans die the same, the place they go after death isn’t decided upon by a god it is Mu (nothingness).
~ Ryuk about death.
You have lost, Light. Didn’t I say in the beginning, when you die, the one who’ll write your name down in a notebook will be me? That is the deal between the Shinigami and the first human to get their hands on the note in the human world. Once you enter prison, I don’t know when you’ll die. It’s annoying to wait. Your life is already over. You’ll die here.
~ Ryuk before killing Light.
Once a name is written down in the Death Note, you can't do anything about it. You more than anybody else here should know that. Goodbye, Light Yagami.
~ Ryuk's disgraceful last words in the manga.
It was good while it lasted. We eased each other's boredom for quite a while. Well, Light, it's been interesting.