I have no problem with players not resigning, that is their right.
However if they obviously ought to resign then i usually have fun by promoting every single pawn to Q before mating them.
I'm too impatient for that, once I have sufficient material I'm in a rush to checkmate the king.
I dont worry about people resigning because I am trying to discover the best possible checkmate, the reason I sat down to play chess.
Gotta be REALLY careful about stalemates with that trick.
It depends on my mood. Some times I will try to find the quickest path to mate, which can be quite interesting and fun to do.
Other times, expeciallly when I get the chance, I will try to promote as much pawns to Queens as possible as PerfectGent does. One time I accidently mated my opponent on the middle of the board after promoting another pawn (making sure to avoid stalemate by promoting with check each time) 
It can be a bit annoying if the opponent takes the max time to make forced moves though.
It depends on my mood. Some times I will try to find the quickest path to mate, which can be quite interesting and fun to do.
Other times, expeciallly when I get the chance, I will try to promote as much pawns to Queens as possible as PerfectGent does. One time I accidently mated my opponent on the middle of the board after promoting another pawn (making sure to avoid stalemate by promoting with check each time)
It can be a bit annoying if the opponent takes the max time to make forced moves though.
lol, I've done this as well. Accidental checkmates are so
Yeah, especially if you have some more pawns to promote 
I just keep on playing until they resign or get mated. It's foolish to take this too seriously or get pissed off, although I admit I occasionally get annoyed. However, playing out easy wins rarely involves too much time or effort and counter-balances the games I'm getting my a** kicked in!
As for rematches, I often challenge players who beat or drew me to a rematch, I usually don't offer a rematch to my victims unless they are higher-rated although I usually accept rematch offers made to me if my gameload isn't too high
I don't think I'd refuse a rematch strictly on the basis of someone not resigning in a lost position.
I just keep on playing until they resign or get mated. It's foolish to take this too seriously or get pissed off, although I admit I occasionally get annoyed. However, playing out easy wins rarely involves too much time or effort and counter-balances the games I'm getting my a** kicked in!
As for rematches, I often challenge players who beat or drew me to a rematch, I usually don't offer a rematch to my victims unless they are higher-rated although I usually accept rematch offers made to me if my gameload isn't too high
I don't think I'd refuse a rematch strictly on the basis of someone not resigning in a lost position.
Best? answer ever??
I only get annoyed when a player has routinely been moving at a fixed rate (say, once every two days in a 4 day per move game), then when he's losing he expands that to 3 days, 23 hours. That player also plays on and on. Almost all of my opponents are +2000 strength, so they are good enough to know whether the position is hopeless.
That extra 47 hours per move isn't going to change the position. The effects of their changed behavior are: I lose respect for that person and I won't offer a rematch.
If this site had a public pillory, I would also make sure their name made that list with clear examples of their behavior.
Having said all that, I haven't run into that problem yet in correspondence chess on this site (knock on wood).
So far, All??, opponents on Chess.com have been, fairly, polite .. and None? have done the Stall Tactic described above
That said, on Gameknot.com was Accused of this once? Largely because of being unwilling to resign 15? moves into the game
$#(&$!@#(^%#!@
Yet another Resignation .. Is it just THAT annoying playing against Ish???
It's ANNOYING
Yes, it looked 90% like a Lock for Ish to win, but hadn't even planned out the Death Blow yet ..
Meanwhile, Resigners may Rejoice .. Ish resigned from a Match .. It was clear the opponent had NOT screwed things up, and Death was pending
i usually give them a rematch, then mercylessly beat their pieces to tiny little plastic bits with my queen!
WEll, mk_ that certainly scares me to play you. :)
sometimes i throw my chair at my cousin if he does that!
*continues progressively Obliterating MK*
I hate people like that ! Althought i must say i never resign in bullet games
resigning is a sign of weakness!!!!!!!
yep... gets em every time hehe...
Will resign when clearly one/two moves from Mate .. sometimes
It does seem that quite a few times when playing Super Ratings .. easy mistakes are made by Ish's "betters" .. and Ish has been having the same tendency
resigning is a sign of weakness!!!!!!!
qft
I dont worry about people resigning because I am trying to discover the best possible checkmate, the reason I sat down to play chess.