There's a great science fiction book series called "Perry Rhodan", which explains the whole time travel thing very convincingly, but I think it's only published in a few (European) countries. Too bad, it's really great.
Well, let's imagine Dumbledore uses the TT to go back 60 years and kill young Tom Riddle. That would change SO much - the most obvious changes would be that the Chamber of Secrets wouldn't have been opened by T. R., Hagrid wouldn't have been expelled, there would have been no Lord Voldemort, the Riddle family wouldn't have been killed - many, many people wouldn't have been killed -, etc.
But then it would not only change much, but almost
everything. Maybe, in a world without Voldemort, Dumbledore falls out of the window and dies in 1964. That could happen, you know, because everything's different. Perhaps in the "real" world Tom Riddle said something mean to a first year, who thereupon lost his self-confidence and didn't start to play Quidditch. In the Time Turner-world, there's no T. R. to say mean things and the first year turns out to be a great Quidditch player. Now let's get back to Dumbledore - say it's 05/15/1964 and he's standing at some window (maybe he wouldn't have been there if he hadn't used the TT!) - the promising Quidditch player throws the Quaffle and - hits Dumbledore. Dumbledore falls out of the window and dies. Ok, that was one strange example, but I hope you get my point
Now there are the huge and obvious changes. But there are a lot more not so obvious: Harry's parents worked for the Order. In a world without Voldemort, there is and was no Order - James had a lot of money, so he didn't have to work. Maybe James is bored to death now because he has no job and becomes an alcoholic or something. Harry would not be Harry, because he would be born two weeks later. He wouldn't wear glasses. He would dye his hair green and beat up people who like orange juice.
And - so - on. The Longbottoms, the Weasleys, all the killed families,...
Now I hope you understand what I mean - the consequences would be incalculable because so many things depend on Tom Riddle being alive.
Moreover I do believe that, if time travel was possible, you could only do things that are meant to happen. It's not like you're actually changing the future or the past, it HAS TO happen like this.
You see that in book 3 when Harry realises that he must conjure a Patronus to save his own life. Harry saw the Patronus before he went back in time. Besides, they didn't really change anything. Yeah, now I'm getting to what I want to say. If you read that chapter again, you will notice that they only thought Buckbeak had been killed etc. The things Hermione and Harry hear match with the things they heard before. They have to rescue Buckbeak and conjure the Patronus because it does happen like this. It's like they're only fate's marionettes.
To come back to the Perry Rhodan books, there they use a time travel thingy to go back in time and install a time bomb in a huge computer-like machine. The machine should work some thousand years, as it did before they went back, and then explode in their time, a few days after their travel, because there's no other way to avoid the security system. So there are no other consequences for the future (the future seen from some thousand years ago!) - the computer will work and everything will happen like it has to happen and then it will explode in the present and nothing from past will be changed. It then occurs a bit different and the machine isn't destroyed, but will obey them, but what I said is pretty much what it's about.
Therefore it is impossible to actually change the past.
Oh my god, that was long
Please forgive me possible slips and repetitions.