1) I would never ask an oppenent to resign.
2) If being destroyed, I will resign. There are games that become hopeless and from which there is nothing left to learn OTB. They never reach an endgame.
3) If losing (even clearly and obviously), I will almost never resign (at least until it reaches 'obvious even to a fool' status). If I am going to lose I want to learn more about how play as stiff a defense as possible. More importantly, I want to see the moves and combinations that finish me off.
3A) It is with no disrespect that I do not resign these lost games. It is with full respect. Most oppenents understand. A few have pretty bad attitudes if you don't quit when they think the time is right. These aren't the sort that I want to be playing very often anyway.
4) Good point earlier about playing out K vs K + B + N. Your opponent has only 50 moves to seal the deal or it is a draw. I may not make them play it to mate, but will play through at least 'proof of technique'. It only takes a couple of minor errors to botch this forced mate. I've seem some really good players blow this basic endgame. There a lot of strong players that work hard on openings, followed by combinations and traps, and expect to have such a strong position that they win a ton of games from resigning players. These players often have weak endgame skills.
5) I have played many games where I wish that my oppenent would resign; situations where they can't possibly be learning anything but play hopeless games all the way to mate. I just adjust my mindset and finish them as efficiently as possible.
6) If an opponent drags out a game just to drag it out, we won't play again if they are a fair bit lower rated. If a fair bit higher rated, I'll give them another go - working under the assumption that they are better than I am and worth losing to next time (or worth beating again).
7) I don't mind losing - but I do expect to see proof of endgame technique, and if I can learn some more of it myself at the same time, then it is foolish to resign too soon.
I agree with all but your #3. There's a fine line between chances and no chances. It's always a judgement call depending on position and perceived strength of my opponent. I've resigned down a pawn and position, down a piece with many left, but I've also kept playing down worse because I've had reasonable chances of counterplay and/or my opponent hasn't exhibited strong technique. If they are not a paid member, I'll even go for the timeout. I'm not overly proud.
Players who don't resign only really bother me in tournaments. Not only are they not respecting me but the whole group.
I've never asked or hinted that a player I'm playing should resign and I never will. I've pm'd a few on behalf of others (without their request) though.
i will not unless you have demonstrated that you know how to execute the win. there are plenty of master games where one player is down on pieces but doesnt resign if a draw can be accomplished or the position is exceptionally strong. people who say they resign when they are down a couple of points say that it because they respect their opponent. i say more often it is because they dont respect their own game.