If you take computer evalutations as an example then you should resign when it's like +4-5 without compensation. In my opinion you shouldn't resign if there is any counterplay or you have the possibility to create counterplay.
Resign, or Fight on to the Bitter End?

A person should resign when it becomes obvious that one should resign. There is no 'hope' in chess. There is logic and rarely does luck play a role.

https://www.chess.com/news/the-minor-pieces-spate-1560
That proves that you can still win even after losing a queen! Played by Francisco Toldos rated 2047.

I think it would depend on ranking. My competition and I are at a low-level. We are at this level why?
-We blunder more often and we blow end games more often. So at my level I play them to the end. Either I will win/draw on my opponents error, or I will learn by watching him, how to play a given end game.
By contrast if you are at a level where people are fundamentally solid, then yes, resign and save them the busy work.
In blitz anything goes but in standard I make myself resign if I hang a piece. I don't care if I could still win. I want to improve and hanging pieces then trying to steal a game I have no right to win just seems like a waste of time. If I wanted to win I shouldn't have blundered.

How many games will you ever win/draw by resigning?
0.
How many games will you ever win/draw by fighting to the bitter end?
more than 0, believe me.

How many games will you ever win/draw by resigning?
0.
How many games will you ever win/draw by fighting to the bitter end?
more than 0, believe me.
True,true. But if you are two pieces down, then you should resign.

How many games will you ever win/draw by resigning?
0.
How many games will you ever win/draw by fighting to the bitter end?
more than 0, believe me.
This is true, but is it worth the effort to fight to the bitter end to win perhaps 10% of my "lost" games? It won't be my skillfull playing that wins the game, but rather a blunder by my opponent, so I learn nothing from the effort.
I prefer to start a new game rather than waste my time trying to salvage what should be (and probably will be) a lost position.


If its recreational then resign when you're down by a significant amount, in tournament play, judge it by your chances of maybe squeezing a win/draw

I've never understood the concept that resigning shows respect. When I'm on the other side of the board (I have the winning position), I'm not bothered if my opponent wants to play to checkmate. It usually takes a short amount of time. Besides, I can use the endgame practice. In fact, many times when my opponent resigns, I input the game into a computer program and play it out.

Here's an interesting position:
It's a win for White, but, from experience I can tell you that it is easy for white to blunder, and for Black to at least draw. If I'm playing Black, do I resign or hang on and hope that White blunders? If I'm in the last round of a tournament and fighting for first place, I would hang on and hope. Otherwise, why continue for another 20 or so moves, just to lose (I usually have a two hour drive home, so I don't like to hang around the tournament room longer than necessary)?

How many games will you ever win/draw by resigning?
0.
How many games will you ever win/draw by fighting to the bitter end?
more than 0, believe me.
I agree. I always make sure that my opponent earns their win. If they're going to walk all over me, I'm not going to lie down to make it easier for them.

How many games will you ever win/draw by resigning?
0.
How many games will you ever win/draw by fighting to the bitter end?
more than 0, believe me.
Silly argument. How many more games will you win by not dragging out lost games and starting a fresh one instead? Way more than you will ever win by playing on after being down a rook or queen hoping for a miracle blunder in your favor ;)...
Playing on in a losing position is just inefficient and ineffectual. You will learn faster and win more games overall by resigning lost positions and moving on.
P.S. Don't bother posting queen sacrifices that are winning positions and then claim they won after playing down a queen. That's disingenuous.
Back in the old days when I first learned chess I was taught that chess etiquette favored, almost demanded, resigning when one's position became untenable, as a sign of respect towards his\her opponent. I interpreted this to mean that when I'm a piece down, certainly a major piece down, (and not in the middle of some spectacular sacrificial attack), I'll usually resign. More and more these days, however, I play against "bitter-enders". Of course, I COULD commit a fatal blunder and lose the game, but...
What do you think? Should you resign (after losing the first major exchange in the middle game, for example), or fight on? Has resignation gone the way of "tennis whites" ?