Why does the Doctor favor and protect Earth, as he is a Time Lord and not from Earth? Is there any canon explanation?
There are a couple of other explanations: - in the TV movie the Doctor states that he is half human on his mother's side. So thus if that is true and his mother is from Earth's future, then by protecting Earth he is simply ensuring his own survival.
IIRC, in the Dr. Who RPG, it is also stated that the Earth is a "temporal nexus point", meaning that changes on Earth have bigger effects on the wider universe, although it is not really explained in any more detail.
And an additional one - we know from episodes like "The Doctor Dances", that the human empire eventually spreads out throughout the entire universe. So destroying the Earth before that happened would leave a void which could be filled by another race.
There are two major reasons that The Doctor favours Earth.
First, the Doctor has, at various points, praised humanity on it's survivability, indomitable spirit, and explorer's spirit (Reference). Even for the episodes that don't take place on Earth, there's usually humans around. Additionally, most of the Doctor's companions have been human. So, the Doctor has likely developed some level of emotion for humanity.
Second, and perhaps more important, and relevant to the new series, the third Doctor spent a period of exile on Earth, being unable to leave for other planets or times, and working with UNIT to defeat various threats to Earth. This, combined with the destruction of Gallifrey, means that Earth is like a second home to the Doctor. That's why he feels it's worth protecting.
Bonus out of universe answer: there's definitely some amount of bias here, as Izkata said. If the Doctor went around praising and protecting some other species, the show probably wouldn't be as interesting or accessible to most/all people.
Here are a few quotes that may explain it.
TIME LORD: We have accepted your plea that there is evil in the universe that must be fought, and that you still have a part to play in that battle.
DOCTOR: What? You mean that you're going to let me go free?
TIME LORD: Not entirely. We have noted your particular interest in the planet Earth. The frequency of your visits must have given you special knowledge of that world and it's problems.
DOCTOR: Yes, I suppose that's true. Earth seems more vulnerable than others, yes.
TIME LORD: For that reason you will be sent back to that planet.
DOCTOR: Oh, good.
TIME LORD: In exile.
DOCTOR: In exile?
TIME LORD: You will be sent to Earth in the twentieth century, and will remain there for as long as we deem proper, and for that period the secret of the Tardis will be taken from you.
-- The Doctor admitting that Earth is more susceptible to evil in "The War Games"
"What's the matter, old girl? Why this compulsion for planet Earth?"
--The Doctor talking to the Tardis when it randomly choose Earth, yet again, as it's destination. It would seem that the TARDIS is following the orders of the Doctor's release and Exile. [Episode, Black Orchid]
"I am just a tourist. I like it here."
--This may be just be a snarky comment, but it's also possible that he is just exploring all of Earth history (perhaps partially against his will, thanks to the Tardis), and fighting evil when he comes across it (as ordered).
The Doctor is something like a thousand years old. What makes you think he spends most of his time with helping Earth?
We probably only see the stuff that's relevant to us. Self-centered humans, indeed...
I have no evidence. But, is it possible, that the Time Lords exiled The Doctor to Earth to basically imprint him into saving humanity because humanity is the future of Gallifrayan/Time Lord kind?
Time Lords survive till the end of time supposedly. The Doctor always says that humans survive, they always survive. Maybe, just maybe, humans are the Time Lords. Perhaps this one small thing was kept from The Doctor. Humanity must survive, because people matter. Humans matter - as do the Time Lords.
(Well it makes sense to me, dunno about you lot.)
I believe there was an episode - I have actually been trying to find it - where the Doctor is asked why he favours Earth. He answers that he was in a bad place in terms of his emotional state after he pretty much destroyed his and the Dalek races when he happened upon Earth. He goes on to marvel at how it felt like home to him.