Every one thinks that the 10th Doctor's "I don't want to go" was a little egotistical and not very Doctor-like, and so did I. But after watching the 50th anniversary special I've had some different ideas.
(Let's assume for timelines sake that the 10th Doctor during the special was in between "The Waters of Mars" and his fight with the Master.)
Everyone knows that when you're about to die, your life flashes before your eyes. Well, what if it does- even the parts you can't remember.
The 11th Doctor told the 10th and the War Doctor that neither of them would remember what happened because the timelines would be to scrambled. But what if, just before 10 was about to die, he remembered the meeting? He had to have remembered a little bit of it as 11 or he wouldn't have known to throw the fez.
What if he also remembered that he was going to go to Trenzalore? That's what the 11th Doctor told him, and the 10th Doctor replied before going into his Tardis, "I don't want to go," his famous last words that brought tears to everyone's eyes.
He doesn't know how long he's going to live. He hears the 11th saying he's about 1200 years old, and the 10th is only 904, give or take, when he regenerates, but how does he know he isn't lying? Even the 11th said he forgot how old he was. The 10th Doctor also meets Clara first. He doesn't know about Amy or Rory or any of the adventures he will have with them. He doesn't know how soon he's going to Trenzalore. It could be a year and he'll die at Trenzalore.
He is not saying that he doesn't want to leave this version of himself, even though I will admit he is egotistical. He's saying that he doesn't want to go to Trenzalore. He doesn't want to die. He doesn't care about this regeneration. He means the Doctor in general.
Now, the fact that he was in his Time Lord Victorious phase during the 50th anniversary and when he died, maybe he did mean it egotistically, but I love the 10th Doctor to much to not speculate that Trenzalore had something to do with his last 4 words.