A classic situation is the "Go back in time and kill my dad" example:
If you go back in time to kill your dad, and succeed in doing so, then your dad wouldn't meet your mom and they wouldn't give birth to you, so you wouldn't be alive to have a desire to kill your dad, and you wouldn't be alive to go back in time, and you wouldn't be alive to kill your dad.
According to that logic, you CANNOT kill your dad. You can go back in time, you can try to kill your dad, but realistically something MUST HAPPEN TO KEEP YOUR DAD ALIVE.
In fact, it's likely that your attempts to kill your dad are what steers him to your mom. In that case, not going back in time is also impossible because attempting to kill your dad is somehow related to your existence.
A lot of manga uses the "time travel" device to solve inconvenient plot issues, and after its first use a precedent is established that it works. But for me, as a reader, my suspension of disbelief ends there, and I can't enjoy the series anymore because I keep asking the question: How are you still in existence after altering the established timeline?
I don't accept the detached parallel universe theory either.
Not all manga uses time-travel, but since Negima and Ganota ended and it looks like Bakuman might be ending soon in the near future, I'm specifically looking for a time-travel related story that I can accept. Ideally, time-travel will be central to the progression of the story, but I'll accept pseudo time travel (like Emanon or Hajimari no Niina) or stories where time-travel happens on less than 2 occasions.
EDIT: Simulated consequential realities don't count. i.e. The character wishes to change something, and then is placed in a world where that change becomes reality to see the consequences of that change, usually an illusion or dream created by a greater power to persuade the character against their original wish.
Edited by DJ Fatalyst, 15 April 2012 - 07:11 PM.