I heard someone say GM Fischer never resigned. Maybe it was almost never.
NEVER RESIGN!

Well, conceivably you could know with 100% certainty that a position is objectively lost (not necessarily implying ignorance about chess, in other words), yet play on anyway because even if the extremely low chance (could be 1 in a quadrillion for example) of you not losing doesn't occur, your result does not worsen compared to what it would have been had you resigned.
So when you wait to see if an extremely unlikely thing will occur in a riskless manner, it doesn't necessarily matter if that unlikely thing never, ever happens because your result will not get worse in any way.
The main factor, then, is time -- if you spend 10 minutes trying to not lose a position where there is an extremely low chance of not losing, your result will not worsen, but you have spent 10 minutes with no improvement of the result, when those 10 minutes could have been spent elsewhere. But people have their own motivations for spending their time -- maybe those 10 minutes were just awesome, as you got to witness the technique step by step. For others, taking those 10 minutes is just not worth it. I would say most of the time a person who resigns late just wants something as close to total confirmation as possible; although the opponent being annoyed at spending more time on a position than he would like could be a by-product of this, this could be considered more of a side effect, rather than the main intention of the person who played on. Obviously a person who only does it for the thrill of the fact that their opponent has to spend more time than he would like, does not have very good intentions.
To tell someone to resign is to say that your conception of what is a waste of time and what isn't is the one that should be followed, without regard to the opinion of your opponent. Not to say that the opinion of the opponent is "correct" either -- if both players disagree on when the game ought to finish, the game can eventually be decided by checkmate or a time win, an objective rule.
If someone plays on against me when I'm up two queens, I'll just figure out how to make use of them in order to force checkmate, ideally in an efficient manner. I will not assume that my opponent thinks I can't win it, but instead keep open the possibility that he thinks there is an extremely high chance that he will lose, but figures he can find out for sure in a risk-less manner. I'm fine with giving him that confirmation. Maybe he really does think I can't win it, but again, I'm not just going to assume.

Well, conceivably you could know with 100% certainty that a position is objectively lost (not necessarily implying ignorance about chess, in other words), yet play on anyway because even if the extremely low chance (could be 1 in a quadrillion for example) of you not losing doesn't occur, your result does not worsen compared to what it would have been had you resigned.
So when you wait to see if an extremely unlikely thing will occur in a riskless manner, it doesn't necessarily matter if that unlikely thing never, ever happens because your result will not get worse in any way.
The main factor, then, is time -- if you spend 10 minutes trying to not lose a position where there is an extremely low chance of not losing, your result will not worsen, but you have spent 10 minutes with no improvement of the result, when those 10 minutes could have been spent elsewhere. But people have their own motivations for spending their time -- maybe those 10 minutes were just awesome, as you got to witness the technique step by step. For others, taking those 10 minutes is just not worth it. I would say most of the time a person who resigns late just wants something as close to total confirmation as possible; although the opponent being annoyed at spending more time on a position than he would like could be a by-product of this, this could be considered more of a side effect, rather than the main intention of the person who played on. Obviously a person who only does it for the thrill of the fact that their opponent has to spend more time than he would like, does not have very good intentions.
To tell someone to resign is to say that your conception of what is a waste of time and what isn't is the one that should be followed, without regard to the opinion of your opponent. Not to say that the opinion of the opponent is "correct" either -- if both players disagree on when the game ought to finish, the game can eventually be decided by checkmate or a time win, an objective rule.
That's a game theory-like perspective. But there's also the practical concern of physical energy and fatigue during a long tournament. If you're sure the position is lost and your opponent is more than skilled enough to win it, then giving yourself an extra 10, 20, or 30 minutes to rest between rounds is a very practical decision.

Absolutely. But that's up to the individual to decide. They shouldn't resign simply because their opponent perceives it to be a waste of time, but rather because they do. Of course you can argue it's "nice" to resign because you are making life easier for the opponent; unfortunately though, I just can't comprehend the difference between doing that and, say, purposefully blundering a rook. The point of competition to me is that both sides are at war with one another -- really, I kind of want a fight. In fact it's actually kind of satisfying to checkmate someone, even in a trivial position -- it's like I jumped through every last obstacle and proved everything to my opponent 100%.
I'd love to do that against a national master or something who was hoping I would crack or something; I really would . Recently at a tournament I saw an NM play on until one move from mate against a 1700 in the position king and rook vs king (there was time pressure, but it's still quite simple). I bet that trivial mate was damn satisfying for the 1700 to pull off -- he proved himself, all the way through.

And I'm not playing devil's advocate on that one: I really do get satisfaction from checkmating people -- not necessarily more satisfaction than if they resign, but it is satisfying in its own little way. I generally don't play until mate, but the former is true. If the position is truly "trivial," I don't really have to expend many brain cells to win it and it all feels rather painless.

I dont often resign, sometimes for an early queen blunder or if I am not playing well, losing and not enjoying the game. I am a beginner and I enjoy playing out losing and winning endgames to mate.
However, I dont play correspondence chess and I can definatly get why people not resigning a hopeless positon is annoying in that context. But the rules of the game are there for everyone to know and follow and if someone was to exercise their right to play on to mate then so be it.

Yes -- that double feeling has happened to me a lot. For example, in the following game my IM opponent resigned to me -- sure, my position is winning, and it's not extraordinarily tricky, but in my experience with training sessions with houdini, if the defense is played perfectly, it's still possible to get tricked -- I've messed up positions about as good as that against houdini before. If you're inattentive for just a move or two, even if you've played well for 40-50 moves (this is a key point -- that's a lot of moves yet the hard work can be erased rather quickly if you're not careful), you can allow surprising tricks for a player good enough to notice them, and it can make the win more difficult and in some rare instances, cause a swindle.
Anyway, what's funny is that on one hand I was really happy that he assured me the win; but on the other hand, now I don't have the opportunity to prove to myself I would have actually won it; now I can only speculate and say that I probably would have won it . So superficially, I'll want a win when I can get it, but honestly in the end it probably would have been more satisfying if it was played out a bit longer, just to make sure I didn't allow any last trick, and didn't have to win only because my opponent made it easy on me when he didn't have to. Of course, perhaps he just resigned because he was frustrated and didn't feel like fighting -- again we can't really know.
Here's the game: http://www.chess.com/echess/game?id=57830322

no, you lose far too often because you resign far too often, exactly what the OP was alerting everyone about.

I enjoy watching tennis on TNN. I've seen so many come from behind wins that I know it ain't over til it's over in competition. I don't resign in chess. I win or I lose and go down fighting.

I enjoy watching tennis on TNN. I've seen so many come from behind wins that I know it ain't over til it's over in competition. I don't resign in chess. I win or I lose and go down fighting.
Oho, usual pointless comparison.
In tennis or other sports, pushing hard to score points makes you exhausted so that it becomes harder to score later on, basically.
In chess, when you start to lose material, it becomes easier for your opponent to win even more.

I enjoy watching tennis on TNN. I've seen so many come from behind wins that I know it ain't over til it's over in competition. I don't resign in chess. I win or I lose and go down fighting.
Oho, usual pointless comparison.
In tennis or other sports, pushing hard to score points makes you exhausted so that it becomes harder to score later on, basically.
In chess, when you start to lose material, it becomes easier for your opponent to win even more.
any clown knows that, but the tennis analogy won't go down well with the pros.

I enjoy watching tennis on TNN. I've seen so many come from behind wins that I know it ain't over til it's over in competition. I don't resign in chess. I win or I lose and go down fighting.
Oho, usual pointless comparison.
In tennis or other sports, pushing hard to score points makes you exhausted so that it becomes harder to score later on, basically.
In chess, when you start to lose material, it becomes easier for your opponent to win even more.
any clown knows that, but the tennis analogy won't go down well with the pros.
You mean the pros don't get exhausted during matches ?
If that's what you mean, you know even less than me about tennis.

no, i didn't mean that, little child. but the unfit ones might get exhausted far more often than the pros.
I played my boss yesterday and was in a 2 rooks and 3 pawns vs. rook, bishop and 3 pawns endgame, my boss had 2 rooks. He asked if i was going to resign, and i said no let's play it out. He had the obvious advantage, but you can learn things better when down material, and you know a mistake can cost the game. Anyway, he made a mistake, and i was up R+B against R. i finally won the game, but we both kinda suck so playing those kind of games are instructive. That game was very poor play on both sides, but fun.

"Sure you might swindle 1/100 games, but is that really worth the time you'll waste on the other 99?"
We know your opinion on the matter, Moses, but whether it is worth it is up to the individual, which is my general point.

Again, I don't, because your opponent's idea of a waste of time needn't be the same as your idea of a waste of time. I don't think it's rude to have a different conception of it.

If I thought the odds of saving a game was 1/100, I would play on. When the odds get truly insurmountable, it's time to resign.
So, if I'm down a rook for no compensation against someone rated 1400, I will play on. In fact, I even won a game where I was down 5 pawns for absolutely no compensation in an official USCF game against a 1400.
If I'm down an exchange for no compensation against a grandmaster, I will probably resign as long as I can't see any possible swindle. Fortunately, there are a numerous swindles that even masters stumble into occasionally.
It's all relative. And it's all about what my realistic chances of getting a draw are. 1/100 chance of drawing is reason enough to play on.
If you never resign you have no idea about chess