NEVER RESIGN.
Never. No matter what. More importantly still, resolve to never resign. Recently I won a game against a master after having chucked two pawns in the opening, leaving my king stuck in the center with my queen-side mostly undeveloped. However, I kept plodding along, and eventually even won the game. Yes, it was a junky quick-chess game, but I have won similar games at Game in 120 against A-players and below.
There are several reasons to not consider resigning. The first is that you can't win by resigning. It's a stupid, obvious, even trite saying, but it's true. Make your opponent prove they can win. Often they will relax after achieving a winning, or even won game, and will start playing non-optimal moves. And in slower games, especially, they will become annoyed, which usually isn't conducive to optimal chess. You are within your rights to do so, and may as well exercise them.
The second reason is that if you don't resign, you won't make a mistake by resigning an equal or favorable position. A few months ago I drew against another master. At some point, though, he played an unexpected move, and I thought I was losing my queen. I very briefly considered resigning, and then remembered my own advice. Looking at it again, I realized I wasn't losing my queen at all. The game continued and after a tough struggle, I scored the half-point. Perhaps I had been helped by the knowledge that a few months before that game, a 1900 had resigned against me because he thought his queen was trapped, even though it wasn't. Oops. Perhaps he wouldn't have seen the saving sequence anyway, but he "took me at my word" when he shouldn't have.
And finally, if you decide before a game to not resign, it saves energy. Resigning is a decision, just like any other move, and it requires energy. If you begin to consider resigning, it becomes a drain on finite reserves of energy available for the game/tournament. Thus deciding to not resign beforehand can save you energy in the heat of battle, especially time pressure. Even contemplating resigning in time pressure is a shameful waste. This is especially true as you get older and have less energy to spare.
All that said, I do resign sometimes. But it has to be really bad, and my opponent has to clearly be strong enough and have enough time of their own that I can't imagine them stalemating me by accident. But generally, I play every game out to mate. And as I've said before, you should expect your opponents to do the same, so don't get aggravated when they do so. It's their right to play on, as it is yours.
Finally, here's an example from the club last Saturday of fighting on beyond all hope, and then getting rewarded for it.
Black to move
White had been completely busted for some time, but played on, hoping for a miracle. White stated that he hoped for Black to march his king up the board and somehow walk into a knight fork, so the spite checks began. Instead, Black,with more than ten minutes left on the clock, played ...Ke6, and White instantly played Re7#. White's dance of joy was most undignified, but quite understandable.
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