Only times I have ever conceeded a game were when I was reduced to no models able to move. Nothing but immobile vehicles left on the board. I have had way too many games where I have lost all but a couple of troops (note; i mean models, not units!) or possibly a single vehicle that has lost all its weapons but can still move. Play them suicidally!
I remember one game, way back in the last few months of third edition where my marine army was wiped out, apart from a single space marine. By turn one. Admittedly, I had had first turn so my last guy was a good distance across the board and I had managed to inflict a few casualties to my opponant's army. Not enough to cause any leadership tests or the like though. My opponant (a great guy who was well known at the time for regularly placing in the Grand Tournaments, now known as throne of skulls in the UK) offered me a graceful conceed. I refused and took every oppertunity to get that last guy killed. From that point in the game there wasn't a single combat phase he wasn't involved in. Somehow I managed to make every save needed (which was helped by my opponants inability to roll high enough to hit him in shooting or combat!) and won every combat, causing all but one of his units to be fleeing or have run off the board by the end of the game. I'd love to say I gave that marine a promotion and a new paint job, but he got stolen the next day...
I also particularly remember a 3v3 40k in 40 minutes game. All that was left of my force by my turn one was a single space marine chaplain and a sergeant with a powerfist. Not much was left of the other two forces I was allied with either. We could have conceeded, but instead my marines decided it would be much better to mow their way through 400 points of genestealers, as mell as doing a fair bit of damage to a couple of the Tau units who had shot their squads out from under them in the frst turn.
I'm sure there were hundreds of other games where I was reducded to not a lot, and subsequently wiped of the table with out the opposing army breaking a sweat, but you don't remember those games. Once upon a time in my LGS there was a competition to see who could wipe my army from the board in the shortest time (15 minutes for a 1500 point game, including deploying armies... that kinda hurt lol), but if I never stuck it out to the end, even when I have no chance of winning, I would never know just what my armies are really capable of. With a bucket load of luck at least lol.
As a lot of previous posters have pointed out, when you are rendered combat ineffective, just have fun with it instead of conceeding. How often do we cheer for the underdog? How many movies are there about soldiers left behind, out numbered, short of ammunition and supplies and fighting for their lives, only to come out victorious? You would be surprised how often you can be reduced to a point where you can't win, but can stop your opponant from winning. A closely fought draw can be just as much fun as a win, so never, ever conceed