Well it is considered to be just plain rude to waste you opponents time in hopeless positions.
To Resign or play on

I would resign if I'm about to lose. For example, I might hav a few seconds on the clock and no immediate way to win, or there could be a ridiculously obvious mate pattern, I would resign (though if I'm that low on time, it won't really matter 'cause I'm going to lose quickly anyway). But, if it's not too far into the game, and it's a complicated position with no clear way to win (or lose), my opponent could blunder. I would have a chance then, so it would be dumb to resign there.

Here's a rare reason to play on, playing a very good opponent I looked at his previous games (losses mostly), I noticed something interesting, he resigned all active games on one day ( about ten). What ever was going on in his life I don't know. It's not the best way to win but it keeps my finger off the resign button.

The most annoying part of resignation is when your apponent resigns as soon as they lose their queen. There is plenty more material to play on.
Sparkx wrote:
What's wrong with playing the game to Check Mate when your down on material or position? If I blundered a piece away, my opponent may do the same, or I might learn from a stronger player. Resignation is an option if one choses to end a game before the end of the game.
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If ever asked to resign just say, "I would, but then I wouldn't get to see your winning technique!"
I don't like to resign. I find that I play a lot better when I'm having the worse position. I sometimes even prefer that.
And I hate when people resign right before mate. Sure the game is over already, but I would want to make the final move. I also hate the other extreme. When they resign without a real reason. I've played with a lot of people who resign right after I've taken their rook. Rook for bishop and pawn isn't that bad.