Against a superior player I will often resign a technically lost endgame unless there is substantial hope for an opponent error that would allow a draw.
Masterful Resignations
How long did you let fritz analyse that? 4. Rxd4 postpones mate for one more move than Be7, which is no biggie, but 3. Qd4?? That doesn't make any sense, why would fritz suggest that at all? Are you sure Fritz didn't tell you to do 3. Qf4? At least that move doesn't lead to a forced sequence of moves leading to mate.
My mistake. A brain malfunction occured.
I saw Qf4 as Qd4 in my mind. 
Below is the continuation by Fritz with the correct move of 3.Qd4. Fritz does force mate soon after 3.Qf4, but not immediately. Mate can be achieved in 15 moves with best play from both sides.
Tim Krabbe has a collection of games in which people resigned in winning positions.
Very nice find. Below is the first example. "Black resigned because he saw he was going to lose the Bd4. He could have won on the spot with 36...Bg1".
I had Fritz 12 play the game out with 36...Bg1. Black could have won. Ouch!
Krabbe's site is fantastic and always a great read. If you like this sort of thing, I'd recommend looking through the other stuff he has there - you can just go to the bottom of the page I gave and click "main chess page".
Actually, my question was more open ended. Here's another way of looking at the masterful resignation. Have you or your opponent ever resigned when there was material equality - but the opening was so horribly botched that you or your opponent found it hopeless to continue?
Recently, I considered resigning in a postion, early in the middle-game, where I had material equality but considered my position to be horrible. I went ahead and played, and for awhile I felt I'd improved slightly - but never to the point where I considered it an equal game. And I did eventually lose. I considered resigning because the player I was playing was at least as good as me, likely better, and I was in horrible position, despite material equality.
I've also hung my queen early and played on. It was against a player I didn't know, with no rating, and he hadn't done anything to impress me that he was a strong player. So I decided that until he showed me that he was a good enough player to convert that material advantage, I'd play. And sure enough, 5 or 6 moves later, he gave me a chance to knight-fork his king-queen. I ended up winning that one despite my early blunder that cost me my queen.
The position on the board matters, but your opponents skill matters, too. Even with an incredibly strong position and material advantage, a brand new player may make mistakes that let the game change. Against a stronger player, it doesn't take nearly as much disadvantage to make the whole thing hopeless.
Uh-oh (more problems with the word "zugzwang")...
There's a problem with my use of the word zugzwang? It's only simple logic that if black, from the beginning, has a won game, then every single one of white's 20 possible moves are worse than doing nothing at all (like I said, an exceedingly remote possibility), since if white *could* do nothing at all, he would be in black's position, and would win. That, to me, seems like the very definition of zugzwang.
lol..."When I use a word, it means just what I choose it to mean"--Humpty Dumpty (in Alice In Wonderland)
Sure, but I chose it to mean what the general consensus idea of zugzwang is, and I don't see what the problem is. Is there actually any problem with how I used the word?
Because zugzwang means that you actually degrade your position by moving, and would chose to forfeit your move if you could, right?
And, in the most incredibly unlikely possibility, let's pretend that chess has been solved, and solved as a win for black. This means that every single move white can do from the start loses. Whereas, if white could forfeit the first move, that would turn the tables, and now it would be black who would be forced to make a move and lose. It would be better for white to be able to make no move.
This is zugzwang, no?
"It's only simple logic that if black, from the beginning, has a won game, then every single one of white's 20 possible moves are worse than doing nothing at all..." - Schubomb
@ Schubomb - Fascinating way of putting it. 
You will here chess players say something like, "improve your weakest piece" or "White is better if this move is played".
Both of these statements are technically not correct, because it's impossible to improve or "better" one's position in chess. You can't properly evaluate a position if you think otherwise. This was something I picked up from reading a book by Dan Heisman. It's a new way for me to see the game. I find it quite remarkable. 
Zugzwang
"There are three types of chess positions:
1. both sides would benefit if it were their turn to move
2. only one player would be at a disadvantage if it were his turn to move
3. both players would be at a disadvantage if it were their turn to move.
The great majority of positions are of the first type. In chess literature, most writers call positions of the second type zugzwang, and the third type reciprocal zugzwang or mutual zugzwang." - wiki
NM Dan Heisman
"One's position cannot be better after a move than it was before".
"The evaluation of a position assumes best play".
"Another simple proof is that even if someone does not make the best move in a position, they could have, and so by playing anything less, the position gets worse, while playing the best move, a player retains the maximum potential for position."
Steinar, you're probably right, questions marks on Qf2 might have been better than exclams on Re1+. However, I was merely repeating the marks that Fischer himself used in his annotations. He gave Re1+ two exclams in this variation.
Thanks for the nice comment, and don't worry, no member points off for spelling my name wrong.