White's time runs out in this position. What's the result according to FIDE rules?

all legal moves lead to a forced win for white, and people wonder why chess does not get recognized as a sport!

While this given position is pretty artificial, all arbiters should come up with the same ruling in that position when white's flag falls. The rules are pretty straightforward in such a situation and it is easier for a human to determine if mate is possible for the side with time.  I won't say that arbiters don't get it wrong sometimes or that all rules are completely clear-cut, but that one is.

The problem is that time is also a factor. But time can not be the only factor, thus rules are in place to prevent a win where no possibility of a win exists for the side with time on the clock still.

the time factor could be reviewed so that a win is given as a win, sadly the chess community doesn't take the rest of the world seriously, yet expects the rest of the world to take them seriously. who knows, change can happen.

I agree with those who say that the result is a draw. For the record, here's the relevant articles from the FIDE Laws of Chess (as of 1 July 2017):

6.8 A flag is considered to have fallen when the arbiter observes the fact or when either player has made a valid claim to that effect.

6.9 Except where one of Articles 5.1.1, 5.1.2, 5.2.1, 5.2.2, 5.2.3 applies, if a player does not complete the prescribed number of moves in the allotted time, the game is lost by that player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves.

I am referring to the diagram in post #1 here. This is the case only if Black is able to possibly land a checkmate to White somehow. Unfortunately, by the rules of chess are such that the side with his/her king under check must do all he/she can to escape the check. In this case, it is rather sad that Black's only reply remaining leads to mate, and White has no other alternatives either.

More specifically, the only ways White can escape the check Qg6+ are by capturing with either knight available, both of which land a check on the Black king (there is no other way). Black's king cannot move since all the squares adjacent are either guarded by enemy pieces or unavailable (there is no i-file or 9th rank for the king to escape), and neither can the 'paralysed' Black rook move, leaving Qxg6+ as the only move left (there is no other way), and in response, White only has Nxg6# as the only move left (there is no other way).

Since White has no choice but to land a checkmate on the Black king (by the rules of chess), White will not even be able to voluntarily let his/her own king get checkmated. Hence, Black will not be able to avoid a checkmate to his/her own king and launch a checkmate of his/her own, and the result is a draw.

In post #9, however, the context is different as Black can choose not to perform the killing blow, and instead, let himself/herself get checkmated. In this instance, White can indeed have a chance (although improbable) to checkmate the Black king, and hence, if Black's flag falls, White wins on time.

Black would call flag and win.

Martin is correct. Both players' moves are completely forced so that the only series of legal moves is that black is checkmated (knights and queens on g6).  White is out of time, but black can't win, so it is a draw.

It's improbable but I'm sure at least one plausible variation could be made to end up in that position.

Position in post 1 is trivially legal. Whether it's plausible or not is another question.

 I agree that there is no legal way black can win so it is not lost for white. Since the only legal continuation leads to checkmate for black white should be declared winner after his flag falls. Since the rules do not provide for a situation like this its up to the arbiter.

IMO there are for more likely positions where the rules for time do not suffice. If in blitz you have a trivial draw in many cases (such as bishop + wrong a pawn) one player can keep on playing until he wins on time. You can hardly claim 50 moves in blitz. I have lost games like that and it is pretty annoying.

There is no room in the rules for arbiter discretion in a case in post 1. The rules are clear. White has no time, black is not in checkmate/stalemate so white can't win. In order for black to get a win on time there has to be a legal series of moves leading to black checkmating white; all legal series of moves lead to black getting checkmated. Therefore,  it is a draw.

Black simply wins by timeout.

The position, once reached, would end the game immediately without regard to the clock since it is win-excluded for Black and draw-excluded. It's the same as if a stalemate or checkmate hit the board, the clock becomes irrelevant.

Maybe I'm misunderstanding what you are suggesting here, but I don't know of any rule that would give that result. Checkmate and stalemate end the game immediately but in the given position,  while the mate is inevitable,  it isn't on the board and when the flag falls white can no longer win, unless the position at flag fall is mate. 

@Zigwurst @Martin_Stahl

The clock is still relevant in the game. Think of it this way. Let's say you are in a marathon trying to win a race. For some reason everyone else in the group gives up midway due to injuries (like just stand on the spot for some reason). You are just 50 metres away from the finish line (far in front of everyone else) when you are in clear first place since everyone else will not reach the finish line, but you also end up retiring due to an injury. Since no one passes the finish line, no one (including you) will get the first prize trophy since no one completed the full duration.

In the game, the moves passed can be treated as the 'distance covered'. You are just a few moves away from checkmate, but the flag drops. The flag in this case takes precedence, even though we know that there are only two possible (and similar-looking) ways to continue the game, both of which lead to mate. I continue my discussion after the following second scenario.

Imagine the second scenario like this. You are answering the final exam question of an exam question, and the teacher-in-charge knows that you are the top student and answer questions almost flawlessly in class. The exam question goes, if x^2 + 10 = 35, find the value of x. The teacher happens to be observing you. You write, x^2 = 35 - 10 = 25, followed by x = sqrt(25) ... FLAG DROPS (I mean time's up). You follow the rules strictly and put down your pen immediately. The teacher will not be able to award you the mark even though the teacher clearly knows that you know the value of sqrt (25), since the time is up before you wrote 'x = 5'.

White fails to clear the game in the time allotted, and therefore, even though he/she is clearly one move away from checkmate, White should not be awarded the win. It is a pity that White is a little too slow. Had he/she played Nxf6+ (either knight) Qxf6+ and held the second knight on his/her hand just before the flag drops with the intention of checkmate, White would have won by checkmate.

I am not so sure of the case where White fails to pick up the second knight in time for the mate (Black plays Qxg6+ and the flag drops immediately before White could pick up his knight).

I understand the rules and role of the clock.

In your final hypothetical, what matters is the position on the board at the time of flag fall; i.e. the move has to have been completed, not in progress. If checkmate/stalemate is not on the board and the flag fall is claimed (or in the case of FIDE rules and the arbiter sees the flag fall) then white can't get the win. The only other question that has to be answered is if black can checkmate by any legal series of moves. If there is a legal series of moves that leads to black getting checkmate, then black wins. If there isn't, then it is a draw.