I would say that resignation is perfectly acceptable as long as 1)
It was preceded by a good-faith effort to play optimally.
2)
All parties who are affected by the resignation agree on its timeliness.
The only times I feel a resignation is discourteous is when it negatively impacts people who were depending on your continued presence; for example, if Japan were to unilaterally resign from a game of Axis & Allies despite the objection of Germany.
boardgames.stackexchange.com/users/71/GWLlosa
Many people I've played with have a "See it through to the bitter end" mentality.
Especially for some of the longer games, like Advanced Civilization, Pax Britannica, and Supremacy.
Then again, in those, the game is multi-player, and one player dropping out will drastically alter the flow of play; further, all three have victory conditions that can change the apparent leader to a loser in even the last turn.
I see nothing wrong with offering a resignation, but I also often see it as discourteous to simply walk away.
My usual experience with resignations in long games is one of two situations: Player has to leave for work.
Generally, if this was known before hand, no big deal.
Player is frustrated, losing, and a jerk; player scatters pieces and/or flips board.
On the other hand, while no one I've played with saw offering to resign as inherently discourteous, neither was it discourteous to ask the attempting to resign player to play it out in multi-player games.
boardgames.stackexchange.com/users/1047/aramis
It depends on the type of game: In a game between two players , I would encourage resigning.
In a game between more players , it depends on the game:
If the game has rules for resigning, or players can agree on a set of rules, resigning should be allowed.
However, if resigning would spoil the game for any of the other players, all players should be encouraged to play out the entire game.
Option 1 is easy: when you're playing chess, there is more honor (and a sign that you atleast understand the game of your opponent) in seeing when you are lost, then in playing on and hoping the other person will make a mistake.
When I see I'm lost
and I'm sure the other person knows he's won, I will usually resign.
Unless when I want to learn from the other player, in which case I'll say "I know you've won, but I want to strengthen my endgame for a bit by watching how you do it" or something like that.
Option 2:
for example in Monopoly, a resigning player could just donate his property to the bank, if the other players agree.
But there might be cases where the other players don't agree, for instance when the quitting player will probably be hitting one player's hotels the next turn -
the other player may feel his odds of winning decrease when the player goes.
One small tip: if you do insist the game is played to the bitter end, take away the bitter .
Grab something to drink and/or to munch on, make jokes, have a conversation.
Thank the player for continuing to play, apologize that he still has to play but explain that this allows the other players to end the game as it is supposed to be played.
boardgames.stackexchange.com/users/387/Konerak
One thing to keep in mind is resigning isn't a means to avoid losing, but a recognition that you have lost - you just haven't finished going through the motions.
In a two-player game, this should be fairly simple - you resign, opponent wins, you start another game.
In a team scenario (like Axis & Allies), the entire team should resign as a group - if a single player just packs up and leaves, the other team members should be allowed to fill in the blank spot.
(Assuming they wish to continue the game).
In a multiplayer scenario, it really depends on how the interactivity works.
Dominion can easily manage a disappearing player, but Settlers can't.
Generally, I'd err on the side of allowing someone to bow out, especially if he knows he can't win, but the ultimate winner is still unknown.
If it's fairly obvious that someone is going to win (or if it really doesn't matter who wins), I'd rather sweep and reset than force someone to suffer through the remainder of the game.
boardgames.stackexchange.com/users/916/Allen Gould
That's funny, I was going to use A&A as a perfect example of a game where I would consider it very rude not to resign, although I was thinking about the Axis or Allied players retiring together as a group
--I agree that one member of an alliance resigning unilaterally would be in very bad taste.
The criterion I use is that a player should resign when it's obvious that the victor is obvious but that achieving the stated victory conditions will take a long time.
A&A is the quintessential example because of how hard it is to captured the "island" of Japan, Great Britian, and North America.
boardgames.stackexchange.com/users/675/Adam Wuerl
In a two player game, the time to resign is when it is certain (or almost certain) that the weaker party will lose, given the playing abilities of both parties.
That could be a disparity of as little as two pawns in chess (at the master level), or a piece, major or minor, for weaker players.
There are some multiplayer games like Diplomacy, where a single player can "declare civil disorder" without substantially affecting the chances of other players.
On the other hand, if you are part of a pre-set "team" (Axis and Allies), it's better to resign, if at all, as a team.
boardgames.stackexchange.com/users/1344/Tom Au
In board games played online that have score values resigning may be considered rude.
For example, if you forfeit in Scrabble Online, you prevent your opponent from scoring, thus ending their opportunity for a high score value (which is tracked and viewable by opponents).
boardgames.stackexchange.com/users/1466/pohsyb
Games that have developed a strong professional circuit generally consider resignation a courteous behavior. Some consider  not  resigning discourteous. This question is about the rest of board gaming: When (if ever) is resigning acceptable?
What is the broader acceptance of resignation?
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boardgames.stackexchange.com/questions/2943
boardgames.stackexchange.com/users/970/MrHen
It depends on the type of game. Resignation is discourteous if it negatively impacts other players. A player should resign if it's obvious to all players that they cannot win, especially in a 2-player game. There is nothing with offering a resignation, but it can also be viewed as discourteous to simply walk away.  For example, it can be discourteous is when it negatively impacts others or would  spoil the game for any other players. It also depends on the type of game. In a game  between two players , I would encourage resigning, but in a game between  more players , it depends on the game. If the game has  rules  for resigning, or players can agree on a set of rules, resigning should be allowed.  One criterion that can be used is that a player should resign when  it's obvious that another player will win, but it will take some time. In board games played online that have score values, resigning may be considered rude.   
There is nothing with offering a resignation, but it can also be viewed as discourteous to simply walk away.  For example, it can be discourteous is when it negatively impacts others or would  spoil the game for any other players. It also depends on the type of game. In a game  between two players , I would encourage resigning, but in a game between  more players , it depends on the game. If the game has  rules  for resigning, or players can agree on a set of rules, resigning should be allowed.  One criterion that can be used is that a player should resign when  it's obvious that another player will win, but it will take some time. In board games played online that have score values, resigning may be considered rude.   