I always resign if there is no way of winning , a draw or stalemate
What is the best option for a hopeless position?

It's entirely up to you. High rated players generally resign in hopeless positions as both a sign of respect for their opponent and to save their strength for later games. If you think there is a chance of getting stalemate, then of course you should play on. Sometimes it can be instructive for a lower rated player to see how their opponent accomplishes the mate. This has been the subject of many previous threads and consensus seems to be, despite a vocal minority incensed at those who don't resign, that you have every right to play on until mate.

It is totally up to you. You can either conserve your strength and time, or make your opponent prove it.

All those comment are really constructive, thanks. But there is always the outside chance that your opponent will make a stuping blunder, and you suddenly have the advantage again. I also have come back from an apparently lost game several times, a) because my opponent made a big mistake, or b) I have stubbonly boxed on and achieved a draw. It's a very hard decision to know when to resign, and one I face often.

What they said is right. Only resign if you're sure you have no chance.
When strong players resign they're sure that their opponent could finish the game blindfold, hanging upside down, after being awake for 72 hours straight, with... with this song blaring and children hitting them like a pinata.
lol, but you get the idea. You have to really believe your opponent wont make a big mistake no matter what.
Usually I would resign if it seems like it would be a waste of my time and energy to continue.
Reasons to continue would be:
1). there is a realistic chance that my oponent might make a mistake (based on their previous play in that game), or not know how to play the endgame we are in (especially if it's a Pawns Ending)
2). I'm only a few moves from checkmate anyway
3). I haven't seen that particular endgame before and it isn't so complicated (to me) that I stand know chance of learning anything from it
It don't mind if an opponent carries on in a game I'm winning, to me the endgame is the best part of the game.

Agree, if your winning it's very satisfying, if your losing it's a very unpleasant experience. However, I totally agree with the idea of not draining ourselves trying to retrieve a lost game when the next game could be a winner for us!

I'm inconsistent depending what mood I am in. In bullet chess I rarely resign unless there is clearly no chance at all. In Blitz chess sometimes it depends on the clock, usually just on my position and my opponent.
Playing a random online opponent you really only have their play in your current game to judge them on which is often not enough to know that they can close the game out without blundering. I had a game a few weeks ago where I played on mostly just because I was stubborn and so irritated at myself for dropping a piece. My opponent ended up blundering the piece back and then another and suddenly I was sailing to a win.
In online chess I resign earlier than in blitz and bullet though. Winning on time is never a factor (obviously it is possible your opponent will time out, but that isn't a viable strategy to play for!) and if I have 20 or 30 concurrent games vying for my time there's no point spending time and energy on a clearly lost position.
The lower the level at which you play though the less likely you should resign because the chances of a blunder are progressively higher. e.g. even things like a back rank checkmate when a rook is all you have left against a bigger army.

For me it's the combination of the factors, position and then rating.
If I play someone lower rated I will play on mostly, just waiting for a single mistake, I won many endgames with less material because my opponents weren't that familiar with those positions or with the other pieces (most players really love their queen, without it playing becomes different)
But If I am without pieces and blocked pawns and my opponent has a rook or better then it's resigning time. If my opponent is equally rated or higher and I am in a material disadvantage of more then a few pawns I will resign quickly as well.

Another "option" - let the clock run down until zero to make your opponent wait, or disconnect. Well, many idiots certainly do this.

Debistro wrote:
Another "option" - let the clock run down until zero to make your opponent wait, or disconnect. Well, many idiots certainly do this.
If it's helpless resign, do you really think the person who destroyed you recently will suddenly destruct?

i don't mind if my opponent plays out a losing position to the end as long as they KEEP PLAYING. Abonding the game is poor sportsmanship, and is childish.
From his excellent book, "The World's Most Instructive Amateur Game Book," NM Dan Heisman gives this advice.
Fire on Board - "The player who is losing wants to create as much confusion and complications as possible so to maximize the chances that the player who is winning will make a big mistake and let the opponent back in the game." The corollary is, "When you are winning you want everything simple and uncomplicated."
With a weak side, most pieces taken, and a checkmate from your opponent a very real threat, what is the very best option? To struggle on trying to get a draw or resigning immediately?