From Secrets of the Masters

Pig Shopowner: “Ugh, who cares who wins? Those three are a disgrace to kung fu.
Oogway: “I think they will all lose, until they find a battle worth fighting.
—While young Storming Ox, Thundering Rhino and Croc street fight

It's so nice to see you've managed to take the most respected art form in China and use it to pursue nothing but fame.
—Sarcastically, to Croc

Oogway: “I know how you can all get what you want. Not just fame and fortune.
Thundering Rhino: “And how's that?
Oogwway: “By changing course. When the path you walk always leads back to yourself, you never get anywhere... [sudden change in tone] Well, good night. We've got a big day tomorrow!
—To Storming Ox, Thundering Rhino and Croc

Thundering Rhino: “Uh, excuse me! [stuck between two cliff faces after Oogway pushed him there] But how exactly does this help us get across?
Oogway: “It doesn't. It helps me. [walks over Rhino and helps him up] And by helping me, you help yourself.
—Travelling over the Bridge of Mists

Remember the path.
—Before falling down a volcano

Well done. I see you found a battle worth fighting for.
—After Thundering Rhino, Storming Ox and Croc

From Secrets of the Furious Five

Monkey, you have shown me great skills but I also sense in you, great pain.
—To Monkey

Oogway: “Stay. Use your skills for good, young warrior. Find the one thing that you were denied so long ago.
Monkey: “My pants?
Oogway: “Compassion.
—To Monkey, before he leaves

From Secrets of the Scroll

We knows the ways of the universe? Where and when a raindrop might fall? How strong the wind will blow? Is it all just an accident? Or could it be destiny?... Accident? Or destiny? Little does Po know that it was just such an accident that brought the Furious Five together all those years ago. This is the story of how the Five came to be.
—Opening narration

Oogway: “She wants to make you proud.
Shifu: “Well, maybe I could be proud if she was doing the correct form. [breaks a tea cup]
Oogway: “Your form
Shifu: “Is there another kind? [breaks another tea cup]
Oogway: “Shifu, an acorn can only become the might oak, not a cherry tree. You must let her grow into what she will be.
—After Tigress loses control of her feline instincts

Oogway: “Shifu, there is a matter of the utmost importance.
Shifu: “What could be more important than preparing for battle?
Oogway: “Food! Let's order in.
—While Shifu preparing to face Boar

Oogway: “The cleaner, the comedian, the dancer and even the little doctor. It was no accident that you found them.
Tigress: “I failed Shifu
Oogway: “Worse. You're failing yourself. No matter how much you try, you will never be Shifu. The question is... Can you be Tigress?
—Comforting Tigress before departing in silence

Who knows the ways of the universe? Accident? Or destiny? That is the secret.
—Closing narration

From Kung Fu Panda

Shifu: “Quote A
Oogway: “Well... I didn't say that
—Upon summoning Shifu

One often meets his destiny on the road he takes to avoid it.
—Musings to himself

Your mind is like this water, my friend. When it is agitated, it becomes difficult to see. But if you allow it to settle, the answer becomes clear.
—Advising Shifu

Shifu: “Quote A
Oogway: “[A short pause, followed by a smile] I don't know.
—Discussing about the Dragon Warrior

Now know this, old friend. Whomever I choose will not only bring peace to the Valley, but also to you.
—To Shifu about the Dragon Warrior

There are no accidents.
—To Shifu about Po falling from the sky

Quit, don't quit. Noodles, don't noodles. [Po looks back at him, confused] You are too concerned with what was and what will be. There's a saying: Yesterday is history, tomorrow is a mystery, but today is a gift. That is why it is called the present.
—To Po

Oogway: “My old friend, the panda will never fulfill his destiny, nor you yours, until you let go of the illusion of control.
Shifu: “Illusion?
Oogway: “Yes. Look at this tree, Shifu. I cannot make it blossom when it suits me, nor make it bear fruit before its time.
Shifu: “But there are things we can control! [kicks the tree and a fruit falls] I can control when the fruit will fall! And I can control...[tosses a peach in the air, leaps up, and splits it with a chop, freeing the seed] ... where to plant the seed... hi-yah! This is no illusion, master.
Oogway: “Ah, yes. But no matter what you do, that seed will grow to be a peach tree. You may wish for an apple, or an orange... but you will get a peach.
—Talking about Tai Lung and Po

My time has come. You must continue your journey... without me. You must... believe.
—Parting words to Shifu

From Legends of Awesomeness

—Saying the one word Shifu thought he would never say, after seeing him defeat Junjie, Ghost of Oogway

From Kung Fu Panda 3

Inner peace... Inner peace... [a single plum petal falls onto his nose] Itchy nose... [he blows it away, only for the petal to float back and he sneezes it away] Finally. Inner peace...
—Meditating in the Spirit Realm

Oogway: “Kai, old friend.
Kai: “Master Oogway.
Oogway: “Our battle ended five hundred years ago!
Kai: “Well, now I'm ready for a rematch.
Kai: “Took you long enough! [chuckles]'
—Facing off in the Spirit Realm

When will you realise? The more you take, the less you have.
—To Kai

It was never my destiny to stop you. I have sent another on that path.
—Having his Chi taken by Kai

Long ago, I had a brother in arms. I was an ambitious young warrior leading a great army. Fighting by my side was Kai, my closest friend. One day, we were ambushed. I was badly wounded. My friend carried me for days looking for help, until we came to a secret village high in the mountains. An ancient place of healing. A village of pandas. Yes, pandas. Pandas who used the power of Chi to heal me. They taught me how to give Chi. But Kai wanted the power all to himself. He saw that what could be given could also be taken. I had to stop him. Our battle shook the Earth until finally, I banished Kai to the Spirit Realm. SHould he ever return to the Mortal Realm, he can only be stopped by a true master of Chi.
—Recount in his scroll

Oogway: “You've grown.
Po: “Yeah. Got to lay off the Panda buffet.
Oogway: “You've grown up. [chuckling] As I hoped you would when I sent the message to your father.
—Meeting Po once more

On the first day we met, I saw the future of Kung fu and the past. I saw the panda who could unite them both. That is why I chose you, Po. Both sides of the Ying and Yang. And my true successor
—To Po

Po: “No, Oogway, don't go!
Oogway: “I'm not going anywhere. I live here!
Po: “Oh, right.
Oogway: “It is you who must decide whether to stay or go.
Po: “Wait, I can go back?
Oogway: “Who knows? I've never tried.
—Parting words