Some people say that they will play the game to the end. But that is exactly why people usually resign; the game came to the end so they resigned. Why continue playing a position where there is no game any longer?

Even chess masters don't resign as long as there is a game going on. That means if there are tactics in the position, traps, counter attack possibilities, stalemate combinations and whatever. But as soon as there is nothing left then the game is over and they resign. It really does make sense in my opinion.

So the crucial point is: When is there nothing left? And that depends highly on the player's playing strenght. Thus a simple advice is: Don't resign unless the game has ended according to your own beliefs and feelings regarding that particular position. Isn't that what people usually do anyway?

An exception could be if there are only a few moves left before the checkmate and the checkmate picture is a beautiful position. Many players will probably like to see a beautiful checkmate position performed on the board. And those extra moves don't really matter. But do not drag it out like waiting 5 days to make a forced move. That is silly. 

Three times in the past week or so I got draws in games in which I was destroyed.  Now this is not why I didn't resign -- each game was against a friend, and the point was the conversation more than the outcome of the game, so keeping the game going meant also keeping the conversation going.  I had no intention of getting a draw in any one of them, with just my lonely king against a myriad of power pieces in two of the games, and against a king and queen in the third.  Yet this is still how these games turned out.  Go figure.