What particular speeches do you find to be the "big" speeches of Doctor Who? There are some that just seem to epitomize the Doctor's character.
1) During all the years I've been taking care of you, you in return have been taking care of me. You are still my grandchild and always will be. But now, you're a woman too. I want you to belong somewhere, to have roots of your own. With David you will be able to find those roots and live normally like any woman should do. Believe me my dear, your future lies with David and not with a silly old buffer like me. One day, I shall come back. Yes, I shall come back. Until then, there must be no regrets, no tears, no anxieties. Just go forward in all your beliefs and prove to me that I am not mistaken in mine. Goodbye Susan. Goodbye my dear. ~~~ The Dalek Invasion of Earth
2) Homo sapiens. What an inventive, invincible species. It's only a few million years since they crawled up out of the mud and learned to walk. Puny, defenceless bipeds. They've survived flood, famine and plague. They've survived cosmic wars and holocausts. And now, here they are, out among the stars, waiting to begin a new life. Ready to outsit eternity. They're indomitable. ~~ The Ark in Space
3) In all my travelling throughout the universe I have battled against evil, against power-mad conspirators. I should have stayed here. The oldest civilisation: decadent, degenerate, and rotten to the core. Power-mad conspirators, Daleks, Sontarans, Cybermen, they're still in the nursery compared to us. Ten million years of absolute power. That's what it takes to be really corrupt. ~~ Trial of a Time Lord
4) There are worlds out there where the sky is burning, and the sea's asleep, and the rivers dream; people made of smoke and cities made of song. Somewhere there's danger, somewhere there's injustice, somewhere else the tea's getting cold. Come on, Ace. We've got work to do. ~~ Survival
5) Do you now like I was sayin' about the Earth revolving? [walks toward Rose] It's like when you're a kid. The first time they tell you that the Earth's turnin' and you just can't quite believe it cause everythin' looks like it's standin' still. [looks at Rose] I can feel it. [takes Rose's hand] The turn of the Earth. The ground beneath our feet is spinnin' at 1,000 miles an hour, and the entire planet is hurtlin' 'round the Sun at 67,000 miles an hour and I can feel it. We're fallin' through space, you and me, clingin to the skin of this tiny little world, and if we let go... [let's go of Rose's hand] That's who I am. ~~ Rose
6) 1941. Right now, not very far from here, the German war machine is rolling up the map of Europe. Country after country, falling like dominoes. Nothing can stop it, nothing. Until one tiny, damp little island says "No. No, not here." A mouse in front of a lion. You're amazing, the lot of you. I don't know what you did to Hitler, but you frighten the hell out of me. ~~
The Empty Child
7) This is Emergency Programme One. Rose, now listen; this is important. If this message is activated, then it can only mean one thing. We must be in danger, and I mean fatal. I'm dead, or about to die any second with no chance of escape. And that's okay. Hope it's a good death. But I promised to look after you, and that's what I'm doing. The TARDIS is taking you home. [Rose protests] And I bet you're fussing and moaning now- typical! But hold on and just listen a bit more. The TARDIS can never return for me. Emergency Programme One means I'm facing an enemy that should never get their hands on this machine. So this is what you should do: let the TARDIS die. Just let this old box gather dust. No one can open it; no one will even notice it. Let it become a strange little thing standing on a street corner. And over the years, the world will move on and the box will be buried. And if you wanna remember me, then you can do one thing, that's all, one thing. [turns to Rose, his voice no longer sounding projected] Have a good life. Do that for me, Rose. Have a fantastic life. ~~ The Parting of the Ways
8) No. That's your way of doing things. I'm the Doctor and I cured them. That's right! Hey, hey! There we go, sweetheart! Ay? Look at him... Go on, that's it! That's it! It's a new sub-species, Cassandra! A brand new form of life! New Humans! Look at them, look! Grown by cats... kept in the dark, fed by tubes... but completely, completely alive! You can't deny them, because you helped create them. The human race just keeps on going. Keeps on changing. Life will out! Ha! ~~ New Earth
9) I believe... I believe I haven't seen everything, I don't know... it's funny, isn't it? The things you make up - the rules. If that thing had said it came from BEYOND the universe, I'd believe it, but BEFORE the universe... impossible. Doesn't fit my rule. Still, that's why I keep travelling. To be proved wrong. ~~ The Satan Pit
10) There was a war. A Time War. The Last Great Time War. My people fought a race called the Daleks, for the sake of all creation. And they lost. We lost. Everyone lost. They're all gone now. My family. My friends. Even that sky. [reminiscent] Oh, you should have seen it! That old planet.... The second sun would rise in the south, and the mountains would shine. The leaves on the trees were silver, when they caught the light, every morning it looked like a forest on fire. When the autumn came, a brilliant glow though the branches... ~~ Gridlock
11) Oh, might have spent a million years evolving into clouds of gas ... and another million as downloads, but you always revert to the same basic shape: the fundamental human. End of the universe and here you are. Indomitable, that's the word! Indomitable! Ha! ~~ Utopia
I think I'd better stop there. : ) Feel free to add your own!