Would like to nominate this example for Natter of the Year award.
Doctor Who does this all the time, especially in the new series. It was pointed out by Martha in "The Shakespeare Code". The Doctor explained that it was similar to Back To The Future. Except this doesn't make sense either; in BttF, Marty was the one who altered history, whereas in the episode, the witches existed totally independent of the Doctor's travels. The general Hand Wave is that things have gotten really screwy since the Time Lords died off.
In the original series serial "Pyramids of Mars", Sarah Jane asks why they have to stop the villain destroying the Earth in 1915, when they know it's fine in 1980. In reply, the Doctor takes her to 1980... and it turns out to be a desolate wasteland. Apparently, once the Doctor arrives somewhere, he must complete the Stable Time Loop to maintain the "proper" version of history. (In which case, one wonders... and this question has been voiced in the series... why the heck does the Doctor keep traveling around?!) In Blink, the Doctor explains that time, rather than being a linear chain of cause and effect, is actually "a big ball of wibbly-wobbly, timey-wimey stuff." This apparently explains everything.
But if the Doctor doesn't be in weird places in time (say if he dies, ala Turn Left), we get concentration camps. Law of time travel: if no intergalactic weirdo then Space Nazis.
In other words, if the Doctor isn't there... NAZI VICTORY!!
This seems to be at least somewhat consistent. The episode 'Bad Wolf' has the Doctor shooting down Rose's idea of using the TARDIS to head back and change things, stating that when the TARDIS 'lands' somewhen, it and its crew become part of the events as they unfold.
OBJECTION! In the episode in question, the TARDIS did not "land" at all. The characters were pulled out of it via a super-powerful transmat, while it was still in the vortex. The Time Lords' Laws of Time should thus be irrelevant. But, y'know, Timey-Wimey Ball and all that.
Cool your jets. That super-powerful transmat belonged to a race that is at least as Timey Wimey as the Doctor is, and in fact have built time machines that function almost identically to the Tardis. Odds are good they are just as subject to all this as he is.
Lets not forget the volcano not erupting until The Doctor makes it erupt to get rid of the pesky aliens.
And then there's "Fathers Day" where creating a paradox causes giant time-eating monsters to pop up and destroy the new timeline. Or maybe the old one. It isn't really explained, and they're never mentioned again no matter how much the Doctor changes history.
The explanation — Hand Wave or Justified, your choice — is that that particular area of spacetime was made especially vulnerable by the presence of two different copies of the Doctor and Rose. Doctor 2 (the future version of Doctor 1) advises Rose 2 not to appear to her double, but to wait until Rose 1 had left the area to go become Rose 2. When Rose 2 then instead runs in front of a startled Rose 1 and Doctor 1, which hadn't happened "before", the latter two vanish in a Puff of Logic. The original plan was simply to alter time by having Rose be with her "previously"-alone father at his death, which apparently wouldn't have changed history "too much", by comparison. Rescuing your father in the sight of your own past self, conversely, is too much for time to handle.
I don't think changing history was the problem; it seemed like the problem was that Rose eliminated the reason why they took the trip in the first place. If her dad didn't die, then she would have no reason to request that the Doctor take her back to 1987, so she wouldn't save her dad, and... you get the picture. (Although having multiple copies of her and the Doctor present when it happened presumably didn't help much either.)
Would like to nominate this example for Natter of the Year award.