"I give you air from my lungs."
"I'm really glad that worked. Those would have been terrible last words."
"Rose Tyler, you were fantastic. And you know what? So was I."
Nine was the first Doctor I knew. He was the Doctor. Having regenerated out of the Time War, he had a lot of pain to deal with. He was funny and quirky and alien, saving people all throughout time and space, but underneath, there was something darker, a time he deeply regretted. He tried to bury it, but meeting a Dalek brought the Doctor's ghost to the forefront. He destroyed his people to end the Time War. Rose, and the viewer (unless you have spoilers or I just missed something) didn't really know much about the Doctor's past before this. He doesn't like to talk about it, why would he? but having it out in the open makes it easier for him to heal. And Rose Tyler was there to help him. And she could, because he loved her. In the end, it was love that caused him to regenerate. When Rose absorbed all the energy of the Time Vortex by looking into the Heart of the TARDIS, Nine sacrificed himself to save her. It was because of love he regenerated, and that love defined the man he became.
"[Time is] more like a big ball of wibbly-wobbly, timey-wimey . . . stuff."
"I don't want to go."
I have to admit, Ten is my favorite. I love all the Doctors I know, but Ten is still my favorite. He is more sympathetic than Nine, he is funnier, and so much happier. He has Rose. He still deeply regrets his actions during the Time War and mourns his people, but he is able to be happy with Rose, having adventures and saving countless lives . . . until Canary Wharf. "Doomsday:" one of the saddest episodes ever. The Doctor, Rose, Mickey, parallel Pete, and even Jackie a little tiny bit, successfully stop an invasion of Earth by the cybermen and Daleks. Unfortunately, events transpire so that Rose and her family are trapped in a parallel world and the Doctor is not.
Throughout the next series especially, the Doctor mourns Rose. It's hard for him to go on. He lost the girl he loves. He has Martha with him because he is lonely, but she can't replace Rose, nor should she. He still manages to be quirky and hilarious, while mourning Rose, but there are times when it really gets to him. He is better with Donna, they get along well, are just friends, and can really be funny together. They're especially funny when they meet Agatha Christie. But he has not forgotten Rose, or the terrible things he has done in the past. As the parallel worlds collide and the Daleks attempt to destroy all of reality with a reality bomb, all of the Doctor's companions (the ones who appear in the new show up to this point) come back to help him, even Rose. He is so happy to see Rose again, but she can't stay forever. A half human version of the Doctor is created by a human/Time Lord biological meta-crisis with Donna and the Doctor's hand, full of regeneration energy. Born in battle, as Nine was, the human Doctor kills all the Daleks, though the Doctor would have preferred to fix things without bloodshed. The human Doctor has to stay with Rose in the parallel universe, because he needs her, as Nine did. The real Doctor is then forced to be alone . . . Martha, Mickey, Sarah Jane, and Jack all have lives of their own to go live, and the meta-crisis caused Donna's memories of the Doctor to have to be erased so her brain wouldn't burn up. The Doctor doesn't do well alone, which meant he started to go crazy, which developed into the Eleventh Doctor.
"Beans are evil!"
"This is a fez. I wear a fez now. Fezzes are cool."
"I will always remember when the Doctor was me."
I've seen many things saying Nine is a tiger, Ten is Tigger, and Eleven is an uncoordinated cat who falls off the sofa and then claims he meant to do that. He really is that way. Eleven is crazy and goofy. But that's his way of burying the past, as he confesses in "The Day of the Doctor." He has a fresh start at life with Amy Pond, then brings her fiance Rory along to keep from breaking up their relationship. Which works, since they get married. He gets more careless, it sometimes seems that Amy and Rory have to look out for him instead of the other way around. And he runs. All the Doctors run, it's one of their favorite things to say, but Eleven even runs from his own death. And, though a fixed point in time, he manages to fake it anyway, and get married to River Song, Amy and Rory's daughter.
He has another bout of depression after he loses Amy, Rory, and River, which Clara, the Impossible Girl, helps to pull him out of. Then he goes back to the Time War, with the Tenth Doctor and the War Doctor. And he doesn't destroy Gallifrey, but instead sends it out of our universe. After that, though, he ends up living for hundreds of years in one town, protecting its people. Finally, he regenerates again. I can't wait to find out what Twelve is like, coming after living hundreds of years to protect one town, and thus the universe.
So, why do I like the Doctor? He's funny and quirky, he has a soft heart (well, two of them, actually), and he's a hero, though trouble follows him wherever he goes. He's lonely, and so I feel sorry for him, but he helps people and makes people love him. Except the mums. They tend to slap him. "All the mums!" (Though Jackie Tyler did like him later.) And . . . he's the Doctor.