A lot of people have been assuming that the reason River knows the Doctor's real name is that she's his wife. It's obvious that she and the Doctor have a long history together and that she knows him very well, so it seems like a reasonable assumption.
BUT. The Doctor never says, nor does River, that this is the case. And although River tells Amy she is "very good" for coming up with the River-as-Mrs.-Doctor theory, we also know that River can lie convincingly (and even be flippant about it) when she wants to, especially when the truth is too serious, or intimate -- or damning -- to admit.
What if, when the Tenth Doctor says in FotD, "River, you know my name. You whispered my name in my ear. There's only one reason I would ever tell anyone my name. There's only one time I could," He was NOT referring to marriage, but to a time when he was dying -- really, ultimately dying with no chance of regeneration?
IMO, that idea would fit MUCH better with River's stricken expression and repeated apologies just before she whispers the Doctor's name into his ear back in FotD -- effectively, she was telling the Doctor not that she would one day become his wife (although that could be true as well), but something much more shattering for him to hear, that she had been with him when he died for the last time?
Obviously this couldn't just be a coincidence of "Oh, look, there's some person with me while I'm dying, I'll tell my name to them," because River uses her knowledge to convince the Doctor that one day, he will trust her absolutely. So it had to be the Doctor's own choice to have River by his side at his death and to give her the secret of his name, perhaps as part of some sacred Gallifreyan tradition ("only one reason... only one time I could").
I think this theory would also help to explain the very serious look the Doctor has on his face when he's talking to River in FaS about the man she supposedly killed. He's already known all along that River would be with him when he died -- now he's having to face the possibility that she was the one to kill him. However, as shown in the earlier episodes, he also gave her his sonic screwdriver at that time (she tells Ten rather angrily that she didn't pry it from his cold dead hands, and I don't think she's lying about that) so it seems most likely that he asks her to kill him... and you could well imagine the Eleventh Doctor finding that a sobering and unsettling thought, and not one he's ready to explore just yet.
Obviously the details are sketchy here, as I have no idea of the circumstances involved. But I do feel pretty confident about the underlying premise. It seems to fit well with everything we know so far -- though I'm willing to be corrected on this point by people with better memories than I have.
What say you, fellow Whofen?