In The Wedding of River Song we believe we are seeing the Doctor and River exchange vows, accompanied by parental consent and everything, but: the hand-fastening is done between River and The Tesselecta!! So did young Melody marry a Time-Traveling Robot from the future, the Doctor, who was after all inside the thing, or maybe even neither?
Related to: Is the Doctor still married?, but asking whether he has been married to begin with.
The ceremony itself may be of dubious legality or even historical accuracy as it can be observed to have never happened at all (as it took place in an aborted timeline), but the Doctor and River have both been shown to retain their memories of it, and they both consider it to be legitimately binding between themselves.
From "Asylum of the Daleks Prequel":
MESSENGER: There is a woman who wants to meet you.
DOCTOR: That's nice, but I'm married.
From "The Angels Take Manhattan":
GRAYLE: What does that mean?
RIVER: It means, Mister Grayle, just you wait till my husband gets home.
There's no reason to assume that the marriage was legally binding, or even that the "battlefield marriage ceremony" The Doctor performs actually exists.
On top of that, the whole thing happens in a timeline that no longer exists and never happened.
If I had to guess, I'd say that the Doctor made the whole thing up so that he'd have an excuse to tell River a big secret without it seeming weird.
At the end of rebooting the universe when Amy and River are chatting, Amy talks about murdering someone and River says it was in an aborted time line, but Amy says she remembers it so it happened. This is like a hint that the Doctor and River remember their marriage (so its real) and was next mentioned as Amy being the mother-in-law.
