Follow good etiquette. Acknowledge you're lost, resign and play your next game. If you ever play chess people OTB in either rapid or classical chess and you routinely don't resign obviously lost positions, your social standing in whatever serious chess scene will take a dive.
I totally agree with this. Anytime you refuse to resign in a lost position where you're down material with no compensation you're basically telling your opponent you don't think he's good enough to finish you off. What opponent wouldn't feel offended? OK, maybe an exception would be if your opponent is rated 200-300 points lower in an OTB tournament with prize money at stake you could play on and maybe come back and win but if he's rated higher or about equal it's really time to give it up. At the club I play at players typically resign even in Blitz games if the game appears lost. I remember one time an opponent became irritated with me for not resigning when I had a bad position but was only down a pawn.
Wow. What a long thread on here. Coming from personal experience in OTB games as a Candidate Master, even if it seems that one is losing, I don't think one should resign unless there is completely no hope for redemption. Also, there are factors that one has to take into account when it seems that you are losing (or at least at a significant disadvantage):
[1] Any potential attacking chances or crazy tactics the disadvantaged side has. If you have a good attack going, the person with the advantage could be intimidated by it to the point that they give away free material just to stop the attack.
[2] How long have the players been playing for? (If the person with the advantage has been playing for hours, the person with the advantage could be fatigued or burned out to the point that they can easily screw up their advantage).
[3] How complex is the position? (The more complex the position, the easier it is for the person with the substantial advantage to screw it up and hand it over to the other side).