Do you accept takebacks? If somebody playing with you propose a takeback, how often will you accept it? Do you know if takebacks are allowed on tournaments?
Regarding tournaments, according to the FIDE rules, takebacks are not permitted.  Section 4.6:


  When, as a legal move or part of a legal move, a piece has been released on a square, it
  cannot be moved to another square on this move. The move is then considered to have
  been made:


(The rest of section four has more rules about touching a piece, moving a piece, capturing a piece, and the like - but the gist of the answer is there: once a move is made, it has been made.)

Regarding casual games... that's entirely up to you.  In general, I prefer touch move and no takebacks regardless of the game - but sometimes, if it was a very good game, it's nice to say, "sure, you win... but what would have happened if..." and play it out a different way.