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 the prison, I don't know when you'll die. It's annoying to wait... Your life is already over. You'll die here. Well, it was good while it lasted... We killed some boredom, didn’t we? We did some various and interesting things... (Ep. 37)
All S1
Well, Light, it looks like you've lost. Remember how in the beginning, when we first met, I told you that I'd be the one writing your name in my notebook? That is part of the agreement, between the Shinigami who brings a notebook to the human world... and the first human who picks it up. If they put you in prison, who knows when you'd die? And I don't wanna lie around waiting. So, it's all over. You'll die here. It was good while it lasted. We eased each other's boredom for quite a while. Well, Light, it's been interesting. (Ep. 37, as Light dies, the last words in the anime)
Why even bother? What are you trying to achieve by passing judgement on them? I mean, why do you care?
Light: Because I've been bored too, Ryuk. (Ep. 1)
At first I wrote the names of the worst criminals I could think of, like I was cleaning up the world one name at a time, so that eventually no one will ever do anything evil again. And while the truly guilty ones who deserve to be punished for their crimes die of heart attacks, the people who are less guilty but who still make trouble for others will slowly be erased through disease and accidental death. Then and only then the world will start moving in the right direction. It'll be new world free of injustice and populated by people who I've judged to be honest, kind, and hardworking.
Ryuk: But if you did that, it'd make you the only bad person left.
Light: Huh? I have no idea what you're talking about. I'm a hardworking honor student who's considered to be one of Japan's best and brightest. And I... I will become the God of this new world.
Ryuk: It's just as I thought.. Humans are so interesting. (Ep. 1)
Kira, deaths by accident, by disease, designated times of death, it's all just as we suspected. We were right.
L: No, unfortunately, we can only be completely sure after those people they've named are dead. We will continue to monitor these meetings and take note of what they say, how they act, and most importantly whether the people they choose actually die. If we can confirm the connection between their plans and the deaths, then we'll definitely be able to catch Kira.
Light (in unison with Chief Yagami): Ryūzaki!
L (with his mouth full): What is it? There is no need to yell in unison.
Light: I can't carry on knowing these people will die. That's just immoral. (Ep. 20)
Ryūzaki. Do you think that I'm actually capable of becoming a murderer, Kira? Even after I help you catch him, do I seem like that kind of person to you?
L: Yes, you do. I've always thought so. (Ep. 20)
These quotes come from Wikiquote's Death Note pages and are available under the Creative Commons Attribution-ShareAlike License.