Play to the death....or resign?

Well, if your opponent tells you to resign then you have to continue because it is considered bad manners to take advice from others during an on-going game.

Against a good player and in a long time control, I'll keep playing if I have any chance of getting local material superiority that leads to checkmate, pawn promotion, or regaining material.  But if it's a straightforward loss with no such chance, I'll resign.

It ain't over till they all drop back into the box.

You hear me?

I'm a beginner so I guess my point of view doesn't hold much weight.  But I view a chess game as the last battle in a war.  The pieces are people, brigades, divisions....stepping forward as a last stand to throw their life on the line for something they believe in.   As long as there are fighters breathing there is a some chance to out-fight, out-last, out-maneuver, or out-wit.  Resigning absolutely removes that chance, which means absolute defeat. And there is no future in defeat for those pieces left standing.   If you play me, keep advancing until the tip of your sword is at my King's throat, because I'm not quitting.

Although everyone wants their opponent to resign rather than play on in a hopeless game, complaining about an opponent who won't resign is like a golfer whining because his playing partners want him to have to make his short putt rather than pick the ball up and say "it's a gimme."

It really depends on personal preference.

Some will resign too early.  Others resign too late.  However, you will only recognize whether it is too early when you review the game and too late when you realize how much time you wasted on losing.

In the balance of it, neither resigning too early or late really matters much.   Even if you were to resign by accident, your loss against a single opponent will not affect your rating much in the long run.

So it really comes down to how you feel.  

I resign when I'm confident that my position is technically lost and my opponent will certainly converge it to victory. There is no use playing against a 2200-rated opponent in a daily game when being a knight down with no compensation, it is just a waste of time - but getting into a material-equal positionally lost endgame against a 1400 person might be worth playing out, since the potential for a catastrophic mistake there is high. 

when you lose the queen, that is actually a form of checkmate so you should resign there...

It has never happened to me before, but I imagine that I might play on in extreme circumstances for stalemate.

When you sort Mega Database by the number of moves, you will see what happens if you don't resign. Black tortured white 277 moves by just moving around his king, then moving a pawn and again moving his king and so on. After 277 moves, white finally resigned.

I have gotten stalemates in hopeless situations. Still there are times to resign when the outcome is certain. 

Then there the people who lose on time. Can't figure the rational behind that one. 

If I have like 7 seconds left in a hopeless position, that's what I'll usually do (sometimes not intentionally).

Generally, I resign if my position is lost.  But whether or not a position is lost depends on the strength of the opponent.  If you're playing someone you don't think is strong enough to convert the winning advantage to a win, it makes sense to continue.  However, players who seem to believe resigning is somehow dishonorable are tiresome.  It would be poor sportsmanship for a football team to quit and walk off the field because it was behind by too many points to come back.  But that's football and this is chess.  A grandmaster who insisted on playing every lost game until checkmate would be considered a poor loser who wanted to punish his opponents by wasting their time for the offense of beating him.

I never resign in a lost position until my opponent demonstrates that they have a plan to take the "won" position through to a win. Then if it's simple enough (vs the strength of the opponent) I'll usually throw in the towel.

If I merely think I'm lost but couldn't win the game from the other side, I play on. Maybe I'm not lost, or if I am I'll learn something about how to handle that type of position.

 I remember one time when I didn't resign despite being down a Queen and a rook. I continued to play until he he had 5 queens...I got a stalemate. Hahahhahah.

Occasionally in speed chess, if my opponent plays on despite being down a queen and rook -- and I'm in an evil mood, I'll start marching pawns down the board.  But with care not to stalemate!  The point is to punish the obstinate player, not to reward him for his obstinacy.  ;-)

I recently had a bullet game in which I made two queens, and the opponent only had a king and a pawn. I had less than a second on the clock, and my instinct told me: "Sacrifice one of the queens for the pawn and resort to a draw". Nope, my conscious mind told me that I should be able to quickly checkmate the king without wasting time collecting the useless pawn... Well, I lost a couple of moves before the checkmate.

Of course, this is an extreme example. Had I 10 seconds instead of 1, my opponent would have been right to resign.

You posed the question as a binary outcome but that's not quite accurate. Is perpetual check death? Can you achieve that despite being way behind? Etc., etc., etc. Use your best discretion...there is no one definitive answer.