Being older I know the problem, u can only ask, but have to accept your opponents decision.
In a live across the board game it is the same as touching a piece which falls over,or falls from your hand, would you expect your opponent to say ok accidents happen, I dont think so. 
Well if my opponents piece slipped from his hand I would say to go ahead and make another move . I'm sure there is a law about such situations , but surely common sense should prevail.
Yes, I was not talking about chess.com . When I said live online , I meant live chess not correspondance . I don't expect "gifts" or "redos" , I just think everyone should be fair and I would certainly allow a take back if it is an obvious mouse slip. Unfortunately some people want the win above everything else. In fact I frown upon anyone who asks for take backs , and I have NEVER asked for a takeback since Ive started playing more seriously , either online nor over the board .
Most serious blitz ,lightning or bullet players on FICS or ICC, in my experience won't give back mouseslips . Their reasoning for this is that mouseslips are caused by either a player trying to move too fast ( and is therefore akin to a touchmove loss in an OTB situation) or their mouse is defective. Either way if they choose not to give you the move back this is withen their rights. Personally I do give obvious slips back but this is only because I don't take such games 100% seriously.
If someone complains about a non acceptance of a takeback request, my sympathies are always with the request recipient, because the rules are clear when you begin the game.
As much as I often disagree with the monkey - "touch move, nuff said" is a good comment imho.
Castling is considered a king move so you are supposed to touch the King first, however when you dont the arbiter or tournament director will usually not make you move the rook but will warn you and allow you to castle. Was the game you refer to played in a tournament ?
I never request or accept takebacks, over the board or online. I state that in my FICS and ICC user notes so my opponents know that before playing me. I even decline them when someone offers to give me one for ethical reasons.
When you mess up in a soccer game and your opponent scores, why don't they take back the point? Takebacks lead to silly ethical dilemmas: Was their request fast enough? Was it a mouse slip or an oversight? What if I allow takebacks and my opponents decline them? I would rather focus on real chess.
In the 200 games since I stopped requesting or accepting takebacks I've somehow managed to make many brain slips but only one mouse slip.
"I state that in my FICS and ICC user notes so my opponents know that before playing me."
I rarely ever read someone's notes before playing them online. Maybe it's my problem if I play someone without reading their policies, but I think it's a bad assumption that your average opponent knows what's in your notes before playing you.
If there were a better way to convey the message, I would use it. But it's fairly rare that my opponents expect takebacks anyway. What I do often offer beginners who want a closer (unrated) game is a free rook or queen in lieu of takebacks.
I generally glance at my opponent's notes and history before I play them in a long game, but I don't usually bother if it's just a quick blitz game.
I wouldn't blame my opponent, I wouldn't request a takeback, and I wouldn't accept a takeback if my opponent was generous enough to offer it.
Ethical dilemmas only arise if you accept takebacks when you make mistakes, but then reject them when your opponents make mistakes. Back when I allowed takebacks, I was frustrated when one opponent actually did that to me.
"If you don't give back something such as this you 1. Need your life to be validated by that (probably quite little) number next to your user id"
It sounds like you're the one concerned about losing the half point. If chess is a hobby and a game, laugh about this, use the experience as a reminder to be more careful in the future, and realize that in the long run everything balances out.
In the example given by erikido23, both the person requesting the takeback and the person denying it are too concerned with their ratings. All you have to do is ask yourself whether you'd request that takeback in an unrated game. Of course not. There is some argument to be made about takebacks in unrated play when the purpose of the game is to have an interesting challenge as opposed to play out a game where you've hung your queen. But in the posted example, there is no interesting challenge to play out after the takeback.
Personally, I like the no takebacks policy as it is unambiguous. It must be painful to follow, though.
In the example given by erikido23, both the person requesting the takeback and the person denying it are too concerned with their ratings. All you have to do is ask yourself whether you'd request that takeback in an unrated game. Of course not. There is some argument to be made about takebacks in unrated play when the purpose of the game is to have an interesting challenge as opposed to play out a game where you've hung your queen. But in the posted example, there is no interesting challenge to play out after the takeback.
Personally, I like the no takebacks policy as it is unambiguous. It must be painful to follow, though.
It was just an example. You completely missed the point. I didn't put in other pieces cause I would have to make up some imaginary position(which I really don't have the time or energy to do)Imagine all the other minor pieces on the board and a rook. Then there is quite a bit left to play isn't there? So yes this is a case where it would be interesting. Me and the people I play live with give takebacks and such when we play. Not all the time and not that I expect them to give them back. But, it is nice to be able to play an interesting position out.
I wouldn't blame my opponent, I wouldn't request a takeback, and I wouldn't accept a takeback if my opponent was generous enough to offer it.
Ethical dilemmas only arise if you accept takebacks when you make mistakes, but then reject them when your opponents make mistakes. Back when I allowed takebacks, I was frustrated when one opponent actually did that to me.
"If you don't give back something such as this you 1. Need your life to be validated by that (probably quite little) number next to your user id"
It sounds like you're the one concerned about losing the half point. If chess is a hobby and a game, laugh about this, use the experience as a reminder to be more careful in the future, and realize that in the long run everything balances out.
I don't think you quite understand...Sometimes the mouse slips(sometimes a result of slow connection or whatever) SO it isn't " just be more careful". Anyways, I don't care about the rating that I have outside of the fact that I like it to reflect how I am playing-not how my equipment happens to be performing on that night, and because I like playing players at or slightly above my level. If my rating is lower because of stupid crap like that I get less games to play against better opponents and hence less enjoyment.
Why are some people so rude and wont allow a take back of an obvious mouse slip. I know they dont have to but surely it is not fair play to win like that . What are your opinions on it ? Obviously we are talking when a game is being played live online . ( For those who do not know what a mouse slip is , it's when you accidentaly make a move because you let go of the button too early , or your mouse slipped )