The Doctor: (using a sensor) Oh, we've got excitation! And I'm definitely picking up something strange.
Christina: Yeah, I know the feeling.
The Doctor: Call it a hunch, but I think we've gone a little bit further than Brixton.
Christina: And what's your name?
The Doctor: I'm the Doctor.
Christina: Name, not rank.
The Doctor: The Doctor.
The Doctor: The Doctor.
Christina: You're called "The Doctor"?
The Doctor: Yes, I am.
Christina: That's not a name, that's a psychological condition.
The Doctor: Far away. Chops and gravy. Watching TV. Mike and Suzanne, and poor old Tina.
The Doctor: Just think of them. 'Cause that planet out there, all three suns and wormholes and alien sand, that planet is nothing. You hear me? Nothing, compared to all those things waiting for you. Good and home and people. Hold on to that. 'Cause we're gonna get there, I promise. I'm gonna get you home.
Capt. Magambo: It's the Doctor.
Malcolm: Do you mean "The Doctor" Doctor?
Capt. Magambo: I know, we all want to meet him one day, but we all know what that day will bring.
The Doctor: Oh, this is beautiful! Intact, it must've been magnificent! A proper, streamlined, deep-spacer!
Christina: Oh, I'll remember that as I'm being slowly tortured. At least I'm bleeding on the floor of a well-designed spaceship.
The Doctor: I'm the Doctor, by the way, and this is Christina, the honourable Lady Christina, at least I hope she's honourable.
Christina: That Lordship of yours. The lord of where, exactly?
The Doctor: Of Time. I come from a race of people called Time Lords.
Christina: You're an alien?
The Doctor: Yeah. But you don't have to kiss me either.
Christina: You look human.
The Doctor: You look Time Lord.
Christina: Those things are going to turn the entire Earth into a desert. So why exactly are you smiling?
The Doctor: Worse it gets, the more I love it!
Christina: Me, too.
The Doctor: The spaceship's a write-off. but the 200's small enough.
Christina: How does a crystal drive a bus?
The Doctor: In a super-clever, outer-spacey way. Just trust me.
Christina: The aristocracy survives for a reason. We're ready for anything.
The Doctor: Gold!
Christina: Oh, no you don't!
The Doctor: Christina, what is it worth now?
Barclay: Hey! Hey, use this! (holds up watch)
The Doctor: I said gold.
Barclay: It is gold!
The Doctor: Well, they saw you coming.
Christina: But you were right, it's not about the money. I only steal things for the adventure, and today with you, I want more days like this. I want every day to be like this. We're made for each other, you said so yourself. The perfect team. Why not?
The Doctor: People have travelled with me and I've lost them. Lost them all. Never again.
Carmen: Doctor, you take care now.
The Doctor: You too. Chops and gravy, lovely.
Carmen: No, but you be careful, because your song is ending, sir.
The Doctor: What do you mean?
Carmen: It is returning. It is returning through the dark. And then, Doctor... Oh, but then... he will knock four times.
Christina: We could've been so good together.
The Doctor: Christina, we were.
The character Lady Christina interacts very well with the Doctor, and seems to have all the characteristics of a great companion -- she is quick witted, resourceful, highly adaptable, talented, loves adventure and excitement, and, when she gets an inkling of where The Doctor could take her, she is eager to join him. The Doctor fully realizes this, and himself defacto states that she would be a natural companion for him, yet, when she asks him to take her along, he refuses, an echo of what has happened with the loss of both Rose and with Donna. The Doctor is realizing that he "goes through" companions, and, instead of accepting this as a part of his fate, he's attempting to block that steady acquisition and loss out of his life by going it alone. This will no doubt become an issue (and, judging by the prophecy of Carmen at the end, not too far in the future -- no doubt the events that will result in the "death" and regeneration of David Tennant's Doctor), since companions are an inseparable part of who and what The Doctor is, it isn't "right and proper" that he travel without them.
As was shown in the beginning with Rose, they push back the brooding darkness that his experiences force upon him. They keep him grounded in that essential mutual quality that is connective of both Human and Timelord, and inspires his own optimism and faith in the future of humanity. That he will also have a companion in the future is suggested by the "future companion", Professor River Song, in the fourth season dual episode Silence in the Library and Forest of the Dead, both written by Stephen Moffat, who will take over the helm as series director from Russell T. Davies starting with season five in 2010.
That the Doctor needs companions is also suggested by the fourth season episode, Turn Left, in which it is clear that, without Donna's presence, the Doctor would have died, and all humanity would have been destroyed when he wasn't there to save them. The general suggestion of that episode is that, in addition to the humanizing element, they also make him stop savoring the "Wonder of the Universe" that keeps him always going long enough to realize when he needs to Get Out and Save His Own Butt.