Allows someone to undo a previous move--ie take back my last move
Takeback?

Take back games are good for teaching people to play chess though. Not good for actual games. Takeback games are unrated by default.
Takeback? Isn't Chess a sport? If it is, why should takebacks be allowed?
Are there takebacks in football, baseball, or other sports whatsoever?
Depending on who you play golf with, you might be allowed to take a mulligan...

Takeback? Isn't Chess a sport? If it is, why should takebacks be allowed?
Are there takebacks in football, baseball, or other sports whatsoever?
Are you allowed to re-take a penalty shot in football etc when training? The answer is yes. And no, Chess is NOT a sport.
I think there should be a takeback button in live chess. Of course, your opponent must approve each takeback that you request. The reason is: once in a while when I play live chess, my opponent makes an absolutely dumb move (like moving a queen into a square guarded by five of my pieces), not because he/she blundered, but because of mouse slip. What's the point of winning a game like this? A takeback button would greatly help. I myself also made a game-ending mouse slip once, dropping my queen, so it could happen. As long as your opponent approves of the takeback, I don't see an issue with it. Just don't approve any takebacks if you feel against it. But having that option doesn't hurt.

Takeback? Isn't Chess a sport? If it is, why should takebacks be allowed?
Are there takebacks in football, baseball, or other sports whatsoever?
I use the Takeback option for playing Chess Varients with stricter rules about where pieces can move.
I've even used a 'takeback' in a rated game here. It was a very good game when my opponent blatantly hung a piece through lack of concentration, so I made an inconsequential Bishop move, he undid his last move, and I undid the Bishop move. I'll take a good loss over a poor win any day.

Give me all the takebacks you want, but it's not likely to improve my game. I learn better from punishment than leniency.
In the rated games I played on ICC I always gave takebacks to my opponents. Even 2-3 takebacks in a game. Why? Because I want to play chess, I don't care about a rating and I don't like to win just because my opponent made a mouse error or overlooked something obvious. Yes, some games in which I granted takebacks I lost. I do not regret my decision.
Give me all the takebacks you want, but it's not likely to improve my game. I learn better from punishment than leniency.
What if your mouse slips, and you make a move you didn't intend to make? Wouldn't it benefit your learning more if you have the option of requesting a takeback, so you could make the move you actually wanted to make?

I understand the need for a takeback button in unrated live games, but it seems quite absurd in online games, where you have all the time in the world to think about your moves.

It may seem absurd for a competitive game in turn based chess (and I would never use it myself for that purpose).
It can certainly be very useful when you are teaching somebody; like when a beginner misses mate nearly every move. It is far easier to 'takeback' and explain, rather than send them a message, with a link for the game, with an explanation which relies on them looking at the correct stage of the game.
Or send them a message with an annotated game board included, which is time intensive.
Beginners learn far more from their teachers in a takeback game.
The option to request a takeback is not so absurd, since in OTB players can request to take back a move. As long as we all understand that the other player is under ABSOLUTELY NO OBLIGATION to a allow it. I believe in more player optons, not fewer. If two players are comfortable with requesting and granting takebacks, why not -- since it is allowed in the rules of chess. I might allow a lower rated play 1 "do over" in a game but a higher rated player I expect to know what they are doing.

If two players are comfortable with requesting and granting takebacks, why not -- since it is allowed in the rules of chess.
The rules are touch move not takeback. See Article 4: The act of moving the pieces.
Tad Dude--Internet rules for take back could include a mouse slip--now some people may not allow it but others would. In OTB chess if you inadvertently know over a piece you are not required to move it (even with touch move)--how is a mouse slip different? Also the other party has to agree so it is an individual choice
What does takeback mean?
As in Rated, Unrated, Takeback?